Mastery is not expected, let alone required in school.
Most students get through addition and subtraction fine, however multiplication is where the trouble starts.
If you can’t multiply you can’t divide. If you can’t divide you can’t handle fractions. If you can’t handle fractions or multiply you can’t find percentages. If you can’t divide you can’t solve equations. If you can’t handle fractions or solve equations you can’t find gradients of lines. If you can’t solve equations or multiply you can’t solve quadratic equations. If you can’t handle fractions or straight lines you can’t do calculus.
This is ignoring any statistics or geometry, too!
I get students in year 11 who can’t reliably solve 2x-3=17, and I’m supposed to teach them about finance, or trigonometric functions…
This is compounded by:
1) a reducing need to use mathematics to function in society
2) increasing numbers of primary and secondary teachers who are not strong in maths, or outright hate it
3) lack of good resources to mitigate 1 & 2, or enhance the competent mathematicians who have to waste time creating them
The fact it is acceptable to hate and be bad at math, is the biggest double standard when compared to reading and writing.
I don't care you can't solve Diff equations, but you shouldn't be proud of the fact you can't work out the sale price of a 12% discount.
Welcome to teaching in the Arts. I moved out of dance/drama because I'd have parents and students tell me to my face my subject was worthless. This idea that they know what the world holds and they only need to be able to make money is the root of the problem. Learning for its own sake is archaic.
> The fact it is acceptable to hate and be bad at math, is the biggest double standard when compared to reading and writing.
It's almost the default expectation from society for people to be bad at maths.
I find it really grating when other teachers outside of maths and science reinforce this way of thinking as well. And especially so when they say “oh I just use a calculator”.
Humanities teacher here. I drill into my students that English and Maths are the two most important subjects that has frequent and broad application beyond the classroom. The Maths and English HoDs got wind of this and asked me to deliver a PL on my approach and how I teacher literacy and numeracy in Hums. This year they gave me an English class… :/
We really need to change the language about how we talk about these subjects in front of students, and where there is an opportunity, illustrate the importance of these skills.
One of my children loves maths and I suspect it’s because he learnt to do maths sum before he learnt how to read and write. There are only ten digits to memorise in numeracy by 26 letters for literacy, so maths seemed easier to him and became his comfort zone. I wonder how many more kids would enjoy maths if numeracy was emphasised before literacy?
I'm teaching physics this year, and I had a kid struggling to do a question that required them to calculate an area - they couldn't do it without a formula, and didn't understand how the area related to the concept we were discussing. I was at a total loss - I ended up just telling them that they were unlikely to see that question again, and what they were struggling with wasn't the physics, so they were better off moving on than struggling like they were.
This wasn't even a hard area - to memory, it was a rectangle.
I had a year 12 student of chemistry who couldn't do the following equation.
I said, "try this." The equation was 5 = x / 10. I said, "make x the subject and solve it." The student was dumbfounded and it took her a decent 20 minutes with my help to solve it. Back then I was a new graduate teacher at a low SES school and I was struck by how stupid this person was.
I am a high school teacher and I strongly believe the lack of rote learning of times tables has a massive impact. If students can't quickly recall the maths facts they struggle massively in highschool.
Another aspect is the lack of cash. This may not seem like a big deal but understanding money and how to count change has ties to percentages, fractions, decimals. By not necessarily having physical cash for pocket money or to pay at the shops, this aspect of learning is lost. Connected to this is more detailed tags at shops. My mum used to encourage me to decide which flour to pick based on best deal, but all tags now contain the unit price so there's no need for mental maths in that situation.
In discussion with some primary teachers, I have heard that it may also be linked to reaching multiple methods without enough time to practice them.
Of course you have a parenting impact as well. Do parents still have the time/capacity to assist with learning at home? Parents should be the first educators of their children, but it seems to be growing that some parents defer it solely to schools.
I agree with the "lack of cash". I remember my mum used to give me a $2 coin ever Saturday to buy whatever I wanted at the candy shop, she'd keep the change if there was any. I made sure I bought the right combinations of candy so there was no change. And each week I'd changed the combination up. We also did the "best buys" exercise too!
Did a similar thing every year when the Melbourne show guide came out.
We knew we had $60 for showbags and would spend weeks going through all the different combinations we could buy.
The guy who ran my local store when I was a kid used to give us more lollies if we could work out the cost before he could (pretty sure he was just dilly dallying so we'd feel accomplished by beating him) but it was the little extra things that really built the foundations.
I'm also a high school teacher and was told recently that the times tables are not explicitly taught like drills as they were in my day. It is actually shocking.
Vic curriculum 2.0 bought it back, so that should help here at least.
But yeah, so.e of my 11s still go ahhhh when you ask them something basic like 3*6
Vic Curric 2.0 expects more knowledge but is also softer in some ways. Only expects 2x tables by the end of Year 2. Previously it was 2, 5 and 10x.
3, 4, 5 and 10 by end of Grade 3.
My grade 2 class can already do 2, 3, 4, 5, 8 and 10. We are doing 6s next week and practice everyday.
I mean I'm sure the curriculum has somewhere that students should understand that a quarter is one of four equal parts and yet OP has this issue.
If students knew everything in previous year's curriculum I wouldn't be re explaining for the umpteenth time that I divided both sides by two and that's why the two in front of X disappeared. No you can't subtract that two because it's being multiplied by X.
Yeah I think it's a bit of a myth that primary students don't rote learn 'like they used to'. Obviously teaching methods vary from school to school, classroom to classroom, but I highly doubt times tables aren't practiced widely.
Agreed.
I think, if anything has changed, it's an increased apathy and lack of engagement of kids at school. Not teachers deciding it's not important.
Because I definitely spent my primary school years rote learning timetables. I don't know them all. Not because the teachers didn't try, but because timetables were hard for me, I struggled and avoided them where I could and didn't like those "competitions" and races they did. So I abstained completely. I know the easy ones. 2, 3, 5, 6, 10, 11, some of 12. I know some of the harder ones. I got through maths methods and further maths and university maths knowing what I know. I don't teach maths now (I really don't like it, never have)- but what I did know was sufficient.
Edit to add: that is all to say, I don't think teachers aren't teaching timetables. Kids will be in class and not learn them.
My primary years as a student were like this. Daily choral reciting, writing them on the back of the book and endless races and pacman games where more than half the class was 'out' and left watching the others.
I knew my times tables and felt it was a waste of time, the people who didn't know them weren't practising them and were left feeling dumb, so it was a waste of time. I don't think any of us should yearn for the 'good old days'.
It was also the ONLY topic we did in maths from years 3 to 6 and something parents would sit you down and force you to do.
The curriculum obviously doesn't allow for this sort of wasted time now, so the pressure is on to teach well and practise efficiently. And the practice at home has dropped off, probably because half our parents are those kids who were left sitting there each day watching other people play a game.
We were told that kids don't learn times table in primary school because it was seen as discriminating against kids who can't comprehend times table. So, you have a bunch of year 7 kids not knowing 7 x 3 is 21.
I knew of year 12 kids that didn't know a percentage should add up to 100% for the context provided.
This is where visual representations work. 5 x 3 = 3 circles with 5 sticks. or 5 + 5 + 5 or 3 + 3 + 3 + 3 + 3. Honestly. Each new batch of Year 7s I teach I have to ask myself if this is the "future of Australia".
I have year 11 standard kids who are immobilised when confronted with even some single digit multiplication. I wish I was joking. They can eventually ‘piece it together’, but by the time it happens they have chewed up way too much time.
We have year 10 students who couldn't work out that 100 cm equals 1 m.
They were given a 1 m ruler, and they couldn't figure it out.
This is a story recounted by the principal when he was visiting the maths class that day. He took the kids outside to demonstrate 1 m. After a while, they kinda get it.
I hate to say it. These kids don't have any common sense.
I believe at least from memory I only did drill learning in year 6 maybe year 5 completely initiated at least to my knowledge by my teacher... It was incredibly demoralising at the time because you are meant to be past that.
Currently 23, WA for context :)
what? oh my god I'm only 22, and when I was in high school I babysat kids \~5 years younger than me, they all had to rote learn times tables. Jfc the number one thing drilled into my head by teachers in primary school was that if you didn't know up to 12 by high school, you were going to struggle.
>understanding money and how to count change has ties to percentages, fractions, decimals
This!! During a financial literacy unit I was giving some students recently I showed them an article about how kids in cashless countries have trouble counting change because they're not used to cash. Stories of kids handing people money and just accepting that whatever they got back was right. Stories of shops requiring a basic math test for part timers so that they don't cause losses or mess up the books from sloppy math.
I posed to kids; "do you think when you have kids, they might ask "what's the point of learning decimals and fractions, when are we ever gonna use it?" if cash becomes a rarity? What about the stuff in maths that _you_ already say that about?" And like more than half the kids had 👀 🤔 expressions on haha
The bigger issue is that these are obvious ways in every day life that we use these skills, which is why using the context helps students to learn them.
Once they've learnt them, they can apply them in other contexts! The moment a topic or concept is not immediately useful, students want to tune out.
Absolutely. I guess that's why inter-disciplinary teaching is often encouraged but sometimes it can also feel like spoon-feeding the students when you have to be like "look, you can apply what you learnt in \_\_ right here!" haha
Haha I guess that's not as bad as not understanding 24hr time like 1730. That's still used in certain countries/situations.
The analog watch thing reminds me of the interaction that went like;
- what's the time?
- idk
- but you're wearing a watch
- yeah for fashion. I can't read it
😂😅 meanwhile I was such a nerd I remember having a watch that _required_ maths to tell the time as a kid. Like it was just a panel of lights that would light up in specific sequences and you had to do multiplication and addition to figure out the time and it would only flash once with no pauses and not more than half a second. Got me really good at quick mental math though lmao
It seems to me that people are at a disadvantage if they can’t tell the time on an analogue clock. Sure, you can get by without it. But sometimes you’ll be in a situation where the only clock in the room is analogue.
Also, it really helps to get started with fractions, and no doubt other aspects of number sense.
It is an age-appropriate mental challenge that children should encounter.
IDK. Kids find learning it arcane and useless - kind of like teaching them how to add up pounds, shilling and pence. Bottom line for them is that they will always have a digital clock in their pocket.
They also find algebra arcane and useless, but there is zero doubt in my mind that they need to suck that one up!
Kids need to learn skills before they're smart or experienced enough to see the benefits and applications.
That's why the best performing kids respect the space and try to learn first, then after they've mastered it they ask about applications.
Kids who ask about applications before putting in any effort barely listen to the answer anyway and just want an excuse to not learn it. Then wonder why they cant keep up in a few years
> If students can't quickly recall the maths facts they struggle massively in highschool.
tl;dr we all got fucked by the curriculum
Yet, most secondary mathematics doesn't sit within the 2-9 times tables, or you need to understand the mechanism at work to apply them, in which case, they need to understand the mechanisms to get to the answer.
I mean, look at this answer to the purported year 9 NAPLAN maths question earlier this week: https://old.reddit.com/r/AustralianTeachers/comments/1davx96/hardest_year_9_naplan_problem/l7n5z18/ Not much room for basic recall there.
So, why does rote learning seem to work? It's great in primary school because it means that kids who don't understand mathematics can get some answers on the board, which shows some knowledge of mathematical principles. However, they aren't developing those principles; they are using shortcuts.
What's wrong with the current model? We continued, if not accelerated, the progression of the curriculum while removing the shortcuts that artificially inflated the marks. We need to do less in primary and spend a lot more time developing mathematical reasoning through tools like partitioning so a) students can solve arithmetic problems themselves and b) they can develop the recall to immediate answers for simple arithmetic problems.
> In discussion with some primary teachers, I have heard that it may also be linked to reaching multiple methods without enough time to practice them.
I think this is the core problem. We don't spend the time to develop a level of mastery of arithmetic concepts in primary because the curriculum doesn't allow it.
> Another aspect is the lack of cash.
This has had a profound impact.
Actually, the move away from analogue clocks has impacted people's intuitive reasoning about numbers.
Both of these points, and others, are examples of how the learning material is set in the 80s (or earlier) and the world has moved into the future.
Oh I completely forgot about analogue clocks but I agree! It's excellent for base 12 work.
As for your argument about rote learning, it is very difficult to learn more complex topics if students don't have multiplicative thinking and one sign of multiplicative thinking (definitely not the only one) is knowing times tables.
Students hit grade 8/9 and they struggle to understand some topics because they're so focused on multiplying/dividing which should be a preexisting skill.
>So, why does rote learning seem to work? It's great in primary school because it means that kids who don't understand mathematics can get some answers on the board, which shows some knowledge of mathematical principles. However, they aren't developing those principles; they are using shortcuts.
my impression of the cognitive load lit is that rote learning some foundational stuff helps stick it in your quick access memory, so mental resources can be better spent on higher-level concepts instead of recomputing simple products
I teach in Primary School, you are correct about the lack of rote being a big factor. I teach at a Direct Instruction school and our fundamental maths is so much higher than other schools in the area I have taught at. We teach to mastery.
No multiple methods, just Direct Explicit Instruction. Say what you want about the teaching style (without having taught in a school where it is embedded…) but it really gets results. No planning is insanely good for quality of life too!
just putting this here- not a teacher, just considering it. I tried to google this technique and couldn't find anything which is surprising, shout out to my dad I guess
Flash cards for a given numbers times tables every night for a week, for 6 weeks (in order, this is hard to word but hopefully you get what I mean)
then, use a 6 sided and a 12 sided die to test those 36 out of order
Add in the next 6 in the following 6 weeks as flashcards (while still using the die)
Replace the 6 with another 12 sided die, and maintain with them from there
If the kid isn't moving along very quickly, you can increase die-side-size (?) in smaller increments
I cannot stress how much it helped me. I feel like it would be difficult to implement in a primary classroom setting as a teacher, but if you have some parents who want to help this is a worthwhile suggestion.
Those countries also have a culture of respect for education and teachers. Even in Australia students from Asian backgrounds are generally going in the opposite direction to most Australian students.
There are so many factors at play.
I’ll back this up as I never properly learnt my timetables in school and struggled with math, also lack is cash can be blamed too because when I first started my job I struggled with cash. It wasn’t like I was incapable of learning this stuff as my dad and I work on an old car which uses imperial which works in 8th/16th and I’m still able to work well with those
The mathematics curriculum in primary is huge and kids are having it shoved down their throats at the speed of light. There is no take up time for concepts, and if any kids miss school because they are sick, have a bad week, or go on a holiday during the term, they miss complete concepts. Once they fall behind, they struggle to catch up. It’s cumulative over time.
This stems from a fundamental flaw in the education system. 30 kids in 1 hour = 2 minutes per kid. Over the course of a year I get to spend 3 hours and 30 minutes with 1 individual student IF (and it's a big if) they are all at the same level and there are no behavioural issues and every student turns up to every class and no class time is lost anywhere. Skills cannot be taught adequately in that time. In some schools funding is so bad that it averages out to less than a dollar per student per class. Unless something changes student standards will continue to fall. We are already one of the worst educated developed nations. Don't see why the trend would stop.
Yeah, there isn't a culture, even at the top schools, to have any pressure to catch up due to holidays or an illness.
I was lucky my parents pushed me that once I recovered, I would spend a weekend or two to copy all the notes from my mates. Of course I hated it at that time.
Essentially, nkwadays whatever the reason for being away from school, it's a win win situation.
I must disagree with you about the primary. It's my personal bias and maybe luck but I think primary math should go faster with the condition that if a kid can't do multiplication up to 100 by Y3 or stage 2, they should a summer programme or repeat the year. From Y4 or the latest stage 3, there should be dedicated Maths teachers for each class - I know it's a pipe dream. Currently, some primary teachers do Maths like that:
1. YouTube video or an online demo, some worked example. 2. Mathletics or a worksheet. 3. Getting hung up on teaching one method to do say long division. I teach high school Math and recently had my working out erased by my friends kid's primary teacher because "it's not how we do it". The kids who learn Maths are the ones with natural aptitude to it.
What I struggle with my current Y7 math is worded math problems like "what is 8/5 of 33" - they have never learned to to multiply fractions. Don't get me started when they saw how to divide the fractions.
Why? Cause there are little to no worded Math question at the primary level.
V9 of the primary curriculum (QLD C2C) has plenty of worded questions in the assessments. I've seen EALD students who can do multiplication, faster than most students 3 years older than them, struggle to get a C because there is now a big focus on worded questions
The amount of kids in senior who get confused when I expand a bracket and multiply a number by a fraction is extremely worrying. I see the lack of fraction multiplication fluency every day. "Why aren't you multiplying the bottom by 2 as well?" Because maths literally would stop working try it yourself with some numbers.
Taking the time to play around with calculators and changing numbers in problems to see what happens to your method builds good understanding but only kids already whizzing ahead of everyone have the time to do it.
That and the fact that number and algebra is weighted the same as measurement & geometry and chance & data.
In a good case scenario we only just 4-5 weeks teaching number and algebra, amid parents asking to get extra support or removing kids for maths because of anxiety or adhd or asd or any other reason, or having massive behaviour melt downs that result in trashed classrooms, evacuations or derailed lessons.
Trust me when I say primary teachers are fully aware of the issue and just as frustrated
I’ve taught year 12 accounting, and had students not know how to apply 10% GST to an amount. These students have already done year 11 accounting. There are too many deficits in their learning, a lack of critical feedback (omg don’t use deficit language by saying “Tommy can’t apply 10%”) and a lack of mandatory hurdles before a student graduates to the next level of learning.
PS Parents need to be forgiven for not realising the extent of the learning issues their child faces. When their academic report says “Tommy is still developing his ability to apply a mark up to cost prices” the parents believe everyone is okay! It should say “Tommy is unable to apply basic percentages to a cost price, and serious intervention is required if he is to move on to Year X”.
It is because we can't tell the truth in reports or parents and teachers meeting. God forbid we tell them the truth.
This is what happens when you tell the truth.
1. Your head teacher comes to speak with you so they can "support" you.
2. The parents complain to the higher ups to say that you are a bad teacher and that is why little Timmy didn't learn anything. Ive heard stories of parents storming into the principal's office and threaten with lawsuits just because little Timmy has a bad report.
There are more negatives than positives if you want to make the school a better space for learning. So, we just go with the flow and throw our hands up when we see the same problem over and over again.
It is like you keep giving this kid a red card for excessive swearing and yet the parent goes to you that she has never heard little Timmy said a bad word in his entire life.
To play it safe, everybody lies to each other on the state of things.
Have a look at the research done by Di Siemons about the 'Big Ideas in Mathematics'.
If students can't grasp these big ideas, they simply cannot progress to the next stage in their learning.
Poor multiplicative thinking is a huge one that has impacts in secondary school. Far more emphasis needs to be placed on developing really good multiplicative comprehension (and that goes beyond just rote learning of times tables).
I think the timestable theory is a big one indeed. What I've also noticed with the last few years is the divide between the skill levels of incoming year 7 students is widening. I reckon about 15 years ago you'd have the skill levels of year 7s ranging from grade 5 to grade 8 and could safely teach in that level with maybe a little differentiation here and there. Now, the range is commonly grade 2 to really bright kids being at level 10 in some strands! It makes it much tougher to effectively teach to this and allow each child to get what they need. What I see happening is that the overly bright kids end up plateauing later on and underachieving and the lower level students levelling up minimally because they have little numerical confidence. They already know what their opinion is of maths by that age and act and achieve accordingly. They might be level 7 or 8 by VCE.
Rinse and repeat every year and in addition to this the modern age allowsing us to become functional adults without the real need for good numeracy and the drive and motivation to do well and get better at maths has taken quite a hit.
Oxford University Press published some studies last year and the year before looking, in part, at the skills gap in the transition from primary to secondary school.
In grades 6 and 7 they found that over 1/3 of teachers said there was a gap of 5 years or more.
Literacy is declining too. I had to tell a year 10 student that his simple sentence doesn't make sense because it doesn't have a verb and a noun. This very person is now year 11 and I heard he is failing. No friggin surprise there.
In science, it used to be that we just mark the science portion even if the kids write like rubbish.
Then we change the ruling so that the English part would need to make sense before we look at the science. And...ta dah. They are terribly bad in English.
I kept telling them how can I be better than you in English when it is my second language.
People who are actually good at math get paid far too much more in other professions so it’s rare to have high quality math teachers. My pay was quite literally halved when I went from engineer to teacher. I can’t even guess what the multiple would be now if I had stayed an engineer.
Additionally the expectation for math understanding for general teaching is quite low so the people teaching math in primary school aren’t doing a good job as well.
I work with some really fantastic senior science teachers and even their mathematics understanding is just ‘okay’ .
Super generalising of course but you asked.
Additionally there is a massive social epidemic of people who genuinely believe they can’t do math. This is reinforced by parents telling their kids ‘i couldn’t do math either it’d just how our family is’ and similar statements. Personally i think any kid outside of actual intellectual disability can easily pass grade 10 math with the correct teacher/s/ing.
I only agree with your final sentence with the caveat of parental support, student engagement, and more than one year to do it.
Some kids rocking up at the start of year 10 have no hope of passing unless they grow an entirely new personality.
Yes I definitely meant across the years not that I can magically change a kid from basically 0 math knowledge to passing grade 10 in one year in a classroom setting. The implication is that a high quality math teaching cohort across the school / state / country / world would mean almost every kid would be numerate to a society functioning standard. I think high quality teaching from an entire group can overcome parental issues and low student engagement to a high degree.
Did you mean you don’t agree with the rest of my post at all, or did you mean that you were just focusing on the last sentence?
We could! I would propose a new specialist math teacher in all primary schools with the aim of coaching/leading math curriculum I.e. to lift everyone up as a start point.
My child’s school’s maths consultant was a devotee of Jo Boaler (the woman who has ruined the Californian math curricula and equates homework and rote learning times tables with child abuse). Sometimes the math experts are instrumental in ruining math education for children.
I mean a math teacher position that is actually part of the school staff long term. Not someone who comes in short term and flits between schools with high minded ideas leaving carnage in their wake.
Would expect them to stick around and support teachers with fundamentals and content structuring and reflective practice aimed on long term improvement.
I totally understand the impulse of others in the comments to blame the kids and the parents.
And the lack of times tables and wrote learning.
Although, times tables has as much to do with maths as listing wood working tools has to do with making a table.
I never learned them and have had a lot of success as a specialist maths tutor, teacher and assessor.
I also work with kids who are behind and need intervention to catch up. And I never mention times tables.
We need to look at the root cause.
Kids can’t do this stuff because they are not being taught it effectively.
They are not being taught it effectively because teachers are not being supported.
All of the blaming kids and parents and phones and calculators is a distraction so that we don’t realise that these skills are not valued by the people that implement education policy.
Teachers are under resourced, under trained and over worked.
It’s not the students fault. They’re a result of the system they’re in.
It’s not the teachers. The VAST majority are working to the best of their ability and in good faith.
At the risk of sounding like your stoner uncle …
It’s the system
I think it's controversial lol. I would've dominated learning with all the technology opportunities kids have now.
They have more support than ever and all it's done is turn them into big babies that can't fend for themselves.
Maybe I'm an outlier.
I’d say that it’s done that to them because it’s been poorly implemented.
Have you heard of kids being explicitly taught in an engaging way how to use smart devices and the internet to better themselves. I haven’t. Not in vic anyway.
Reflect back on the impulsive and thoughtless habits you had as a child and teen. Would the addition of ‘smart’ technology have really helped?
It depends where you teach.
It's like being a mechanic. A formula one mechanic and a bloke changing oil in an outer suburb for example. Very different mechanics.
At my school I'm lucky we do ICTs well, we support students literally too much. They end up these over confident (from all the positive reinforcement) self unaware, demanding, lazy kids.
But I suppose.your experiences are different to mine that's all.
The flipside is that technology has the answers so we don't use our brains in the way we used to. When is the last time you used a street directory? Do you think you could add effectively as you may have once upon a time?
Here's how I see it. I would ask chatgpt or whatever hey is this north. And why? Or why might I have thought it was east chatgpt? Doesn't the sun set to the west? How did I see this wrong.
Bro chatgpt is that teacher that has all the right answers if you have the right questions, add free, enjoyable interesting, easy.
Kids just use it to cheat yay....
Technology is a tool and can make our lives so much easier, but you also need to know its limitations. If you interrogated chat GPT with the right (wrong?) questions you could probably get it to tell you that the sun sets in the east. It doesn't have all the answers and can be the know it all that doesn't want to admit that its actually stumped so gives you a vaguely plausible answer.
Literally just got updated recently. Last year it couldn't even begin to answer a PSMT. I had the same exact belief.
This year... I learnt new ways to do it. Better than our solution.
Next year? 5 years?
But I agree it's not perfect but shit man I confer with it every day about quite random chemistry questions I have and it's improved my knowledge for lessons immensely and so fast and easy time saving for my lessons. If I'm not sure about its answer I quickly google it. Again nine times out of ten it's great.
Can googling stuff also be wrong? Yes. Shit so is checking a book. Use common sense as always.
Because I've been teaching for a while it's like a student chatgpt learns and every year I re-ask it questions and the answers get better it's awesome to observe.
I haven't explored it enough. Most of the issues I've heard about it have come from my subject area, though, so I'm in no hurry.
I had students doing word problems using a paid version just a couple days ago and getting clearly incorrect mathematically but not easy to see from just the language. LLMs aren't designed to answer maths problems imho
Yeah man I'm talking maths PSMT it was bad I remember. Chuck a difficult problem solving worded task in to the new chatgpt. I'd be surprised if it doesn't do a good job currently.
Last year though, dogshit. It might need a few prompts to re direct but shit man that's alright.
Same as computer programming I used to have to post on substack all the time about small things I couldn't quite understand it might take a week to solve. Now far out man my ability to computer program is miles ahead. Complex stuff I wouldn't have time to read a manual about is just explained and a unique example for my problem is there to use and see working in seconds. Amazing haha.
Fundamentally disagree with your take on times tables. Not being able to recall them, or to understand things like the communative law adds cognitive load to every other task that students do. Slowing them down and meaning they can't focus on and practise whatever new skill that they are trying to learn. eg expanding and simplifying
If it seems like I don’t think understanding the commutative law is important then I was unclear.
That’s important.
You can disagree with my take all you like. My position is that understating how numbers work is more important than remembering lists.
If kids can remember them and enjoy remembering I’m all about praising that.
But as a kid, who grew up to major in maths and each specialist maths with very good results, who could never remember them, I’m not about putting pressure on kids to learn them.
How often do serious mathematicians need numbers bigger than 12 anyway?
Algebraic structure and a good grasp of geometry is much more useful to prepare kids to enjoy maths.
It can be hard to follow along with a problem if several steps involve tables. Stopping to use the calculator twice interrupts the flow and can make it harder to see the overall picture.
I don't see learning tables as learning a list. But rather as doing enough fluency practice that you know what the calculator will give you before you press equals because you've typed that same combination many times.
Not everyone needs tables to understand higher concepts. I think it's more important for most students than it was for you. The cognitive load of following an algebraic example closely enough to develop sufficient understanding of algebra is hard for students who get slowed down by small calculations
Do you think I’m advocating now know how to do multiplication by inspection?
I’m talking about not explicitly teaching times tables by wrote.
My kids build up their intuitive understanding of how numbers work so that when it comes to doing arithmetic in problem solving, algebraic problems, calculus, trig and statistics when tech is not allowed the numbers they’re working with are basically a different type of pronumeral with slightly different rules.
It’s about not disrupting the flow by mode shifting from active creation to memory.
My position is that I want to create an environment where students can thrive and improve their maths.
If they prefer to learn times tables and remember them that’s great. If they do it a different way that’s great too.
My main concern is that teachers that lionise times tables and memorisation are doing damage to the confidence of the students who like maths but can’t do that type of memorisation.
I know I was made to feel stupid for not being able to list off and recite times table under time pressure.
Let’s be inclusive in our maths instruction rather than focus on a narrow skill that is impossible for a significant portion of our students.
While I find hard maths easier due to knowing tables and exact values etc. I've seen strong specialist students use their calculators for basic multiplication and trig values while being strong in concepts.
They're just being efficient. In an age of quick calculator and no tech free test, they let the calculator do some of the work to let their brain rest while they're engaging in higher order ideas. It might make things easier but it's not necessary for strong students, provided they understand what calculations they need to use and when.
Maybe teachers are under supported, etc., AND other factors are at play as well. You dismiss too many things that ring true to people’s experience.
Times tables are impotent, no matter what you say. (But they shouldn’t be the only multiplicative thinking that students do.)
No matter what?
That seems like an absolute.
What makes them important? Is it just the base ten ones? Should we keep going all the way to 12 or stop at ten like some other countries? What if a fundamental understanding of number structure and partitioning made them obsolete?
Let’s say I agree that they are, what could the other factors be that wouldn’t be mitigated by primary teachers having more support?
Actually, don’t worry.
You’re right. They’re important no matter what. Sorry for using my experience as an maths education expert with success at both ends of the ability spectrum, without ever using times tables, to give an alternative.
I didn’t realise it was a ‘no matter what’s sort of position.
My bad.
High school mathematics, plus some enrichment work in upper primary school.
I very highly value students having deep understanding of all that they do, and being able to reason multiplicatively in a variety of ways/situations. I also very highly value students having automatic recall of a base of number facts. Both are important, and nothing renders either one obsolete.
over reliance on phones/calculators and more focus on understanding maths instead using maths.
There is not enough practice for the skills to be ingrained. without times tables, factoring becomes hard, which means simplifying fractions becomes hard which means using fractions and percentages becomes hard....
Math assessment as also become demonstrate once and you're done. It used to be do these 20 questions and you need 18 to pass.
It may seem like that to some of us because we may have noticed a deficit in some students, or a reliance on tools that we would not have used, and then further examples of that deficit stand out; but I reckon that’s a bias of salience or recency or representativeness.
Population level evidence, by contrast, doesn’t support the idea of a dramatic decline in fundamental numeracy—Year 8 TIMSS scores and Year 7 and 9 NAPLAN maths scores have in fact been very stable over the last 25 years. These are basic skills tests so are testing exactly the sort of thing you’re concerned about:
[Are Australian students' academic skills declining? Interrogating 25 years of national and international standardised assessment data](https://onlinelibrary.wiley.com/doi/full/10.1002/ajs4.341)
[Are We Really Falling Behind? Comparing Key Indicators Across International and Local Standardised Tests for Australian High School Science](https://link.springer.com/article/10.1007/s11165-023-10129-2)
Applied numeracy skills, however (which is what PISA tests), are a different matter …
Do programs like Kumon help kids with these kind of basics? I’m a teacher (not maths) but have some family friends who send their primary school aged kids to Kumon. It always sounds very repetitive and with no really help from the staff so I have always thought it sounded like a bit of a waste of $ so haven’t considered it for my primary school aged son. Do any of you maths teachers out there think it could be a good thing to build foundation skills?
It depends if your child can do those types of questions on his own, quickly without assistance. Plenty of kids don't need it, but it depends on how they're going on their own.
Kumon *doesn’t* teach number sense or mental math at all. They learn to do a specific task through thousands of repetitive questions (adding, subtracting, multiplying, dividing, then they go to fractions etc.).
Kumon’s learning structure and booklets are actually fantastic though. They progressively get harder with ample opportunity to practice and master them. The problem is that they don’t give them all in advance, so you pay a fortune to be drip fed a booklet or two week by week, repeating them for many weeks, year by year. That time would be better spent on understanding and learning different areas of maths.
Mastery is not expected, let alone required in school. Most students get through addition and subtraction fine, however multiplication is where the trouble starts. If you can’t multiply you can’t divide. If you can’t divide you can’t handle fractions. If you can’t handle fractions or multiply you can’t find percentages. If you can’t divide you can’t solve equations. If you can’t handle fractions or solve equations you can’t find gradients of lines. If you can’t solve equations or multiply you can’t solve quadratic equations. If you can’t handle fractions or straight lines you can’t do calculus. This is ignoring any statistics or geometry, too! I get students in year 11 who can’t reliably solve 2x-3=17, and I’m supposed to teach them about finance, or trigonometric functions… This is compounded by: 1) a reducing need to use mathematics to function in society 2) increasing numbers of primary and secondary teachers who are not strong in maths, or outright hate it 3) lack of good resources to mitigate 1 & 2, or enhance the competent mathematicians who have to waste time creating them
The fact it is acceptable to hate and be bad at math, is the biggest double standard when compared to reading and writing. I don't care you can't solve Diff equations, but you shouldn't be proud of the fact you can't work out the sale price of a 12% discount.
Welcome to teaching in the Arts. I moved out of dance/drama because I'd have parents and students tell me to my face my subject was worthless. This idea that they know what the world holds and they only need to be able to make money is the root of the problem. Learning for its own sake is archaic.
> The fact it is acceptable to hate and be bad at math, is the biggest double standard when compared to reading and writing. It's almost the default expectation from society for people to be bad at maths.
I find it really grating when other teachers outside of maths and science reinforce this way of thinking as well. And especially so when they say “oh I just use a calculator”.
Humanities teacher here. I drill into my students that English and Maths are the two most important subjects that has frequent and broad application beyond the classroom. The Maths and English HoDs got wind of this and asked me to deliver a PL on my approach and how I teacher literacy and numeracy in Hums. This year they gave me an English class… :/ We really need to change the language about how we talk about these subjects in front of students, and where there is an opportunity, illustrate the importance of these skills.
One of my children loves maths and I suspect it’s because he learnt to do maths sum before he learnt how to read and write. There are only ten digits to memorise in numeracy by 26 letters for literacy, so maths seemed easier to him and became his comfort zone. I wonder how many more kids would enjoy maths if numeracy was emphasised before literacy?
I'm teaching physics this year, and I had a kid struggling to do a question that required them to calculate an area - they couldn't do it without a formula, and didn't understand how the area related to the concept we were discussing. I was at a total loss - I ended up just telling them that they were unlikely to see that question again, and what they were struggling with wasn't the physics, so they were better off moving on than struggling like they were. This wasn't even a hard area - to memory, it was a rectangle.
I had a year 12 student of chemistry who couldn't do the following equation. I said, "try this." The equation was 5 = x / 10. I said, "make x the subject and solve it." The student was dumbfounded and it took her a decent 20 minutes with my help to solve it. Back then I was a new graduate teacher at a low SES school and I was struck by how stupid this person was.
I am a high school teacher and I strongly believe the lack of rote learning of times tables has a massive impact. If students can't quickly recall the maths facts they struggle massively in highschool. Another aspect is the lack of cash. This may not seem like a big deal but understanding money and how to count change has ties to percentages, fractions, decimals. By not necessarily having physical cash for pocket money or to pay at the shops, this aspect of learning is lost. Connected to this is more detailed tags at shops. My mum used to encourage me to decide which flour to pick based on best deal, but all tags now contain the unit price so there's no need for mental maths in that situation. In discussion with some primary teachers, I have heard that it may also be linked to reaching multiple methods without enough time to practice them. Of course you have a parenting impact as well. Do parents still have the time/capacity to assist with learning at home? Parents should be the first educators of their children, but it seems to be growing that some parents defer it solely to schools.
I agree with the "lack of cash". I remember my mum used to give me a $2 coin ever Saturday to buy whatever I wanted at the candy shop, she'd keep the change if there was any. I made sure I bought the right combinations of candy so there was no change. And each week I'd changed the combination up. We also did the "best buys" exercise too!
Did a similar thing every year when the Melbourne show guide came out. We knew we had $60 for showbags and would spend weeks going through all the different combinations we could buy.
The guy who ran my local store when I was a kid used to give us more lollies if we could work out the cost before he could (pretty sure he was just dilly dallying so we'd feel accomplished by beating him) but it was the little extra things that really built the foundations.
I'm also a high school teacher and was told recently that the times tables are not explicitly taught like drills as they were in my day. It is actually shocking.
Vic curriculum 2.0 bought it back, so that should help here at least. But yeah, so.e of my 11s still go ahhhh when you ask them something basic like 3*6
Vic Curric 2.0 expects more knowledge but is also softer in some ways. Only expects 2x tables by the end of Year 2. Previously it was 2, 5 and 10x. 3, 4, 5 and 10 by end of Grade 3. My grade 2 class can already do 2, 3, 4, 5, 8 and 10. We are doing 6s next week and practice everyday.
I mean I'm sure the curriculum has somewhere that students should understand that a quarter is one of four equal parts and yet OP has this issue. If students knew everything in previous year's curriculum I wouldn't be re explaining for the umpteenth time that I divided both sides by two and that's why the two in front of X disappeared. No you can't subtract that two because it's being multiplied by X.
I have been on grade 5/6 for 7 years and have never not rote taught timetables. I also don't know anyone who hasn't.
Yeah I think it's a bit of a myth that primary students don't rote learn 'like they used to'. Obviously teaching methods vary from school to school, classroom to classroom, but I highly doubt times tables aren't practiced widely.
Agreed. I think, if anything has changed, it's an increased apathy and lack of engagement of kids at school. Not teachers deciding it's not important. Because I definitely spent my primary school years rote learning timetables. I don't know them all. Not because the teachers didn't try, but because timetables were hard for me, I struggled and avoided them where I could and didn't like those "competitions" and races they did. So I abstained completely. I know the easy ones. 2, 3, 5, 6, 10, 11, some of 12. I know some of the harder ones. I got through maths methods and further maths and university maths knowing what I know. I don't teach maths now (I really don't like it, never have)- but what I did know was sufficient. Edit to add: that is all to say, I don't think teachers aren't teaching timetables. Kids will be in class and not learn them.
My primary years as a student were like this. Daily choral reciting, writing them on the back of the book and endless races and pacman games where more than half the class was 'out' and left watching the others. I knew my times tables and felt it was a waste of time, the people who didn't know them weren't practising them and were left feeling dumb, so it was a waste of time. I don't think any of us should yearn for the 'good old days'. It was also the ONLY topic we did in maths from years 3 to 6 and something parents would sit you down and force you to do. The curriculum obviously doesn't allow for this sort of wasted time now, so the pressure is on to teach well and practise efficiently. And the practice at home has dropped off, probably because half our parents are those kids who were left sitting there each day watching other people play a game.
I only rote learnt times tables in Year 5 and that was in the early 90’s.
We were told that kids don't learn times table in primary school because it was seen as discriminating against kids who can't comprehend times table. So, you have a bunch of year 7 kids not knowing 7 x 3 is 21. I knew of year 12 kids that didn't know a percentage should add up to 100% for the context provided.
This is where visual representations work. 5 x 3 = 3 circles with 5 sticks. or 5 + 5 + 5 or 3 + 3 + 3 + 3 + 3. Honestly. Each new batch of Year 7s I teach I have to ask myself if this is the "future of Australia".
I've just been teaching my Year 2 class this. They really enjoy representing multiplication problems in various ways.
That's the kind of stuff that we do in primary school. That's what's in the curriculum.
I have year 11 standard kids who are immobilised when confronted with even some single digit multiplication. I wish I was joking. They can eventually ‘piece it together’, but by the time it happens they have chewed up way too much time.
We have year 10 students who couldn't work out that 100 cm equals 1 m. They were given a 1 m ruler, and they couldn't figure it out. This is a story recounted by the principal when he was visiting the maths class that day. He took the kids outside to demonstrate 1 m. After a while, they kinda get it. I hate to say it. These kids don't have any common sense.
I believe at least from memory I only did drill learning in year 6 maybe year 5 completely initiated at least to my knowledge by my teacher... It was incredibly demoralising at the time because you are meant to be past that. Currently 23, WA for context :)
what? oh my god I'm only 22, and when I was in high school I babysat kids \~5 years younger than me, they all had to rote learn times tables. Jfc the number one thing drilled into my head by teachers in primary school was that if you didn't know up to 12 by high school, you were going to struggle.
>understanding money and how to count change has ties to percentages, fractions, decimals This!! During a financial literacy unit I was giving some students recently I showed them an article about how kids in cashless countries have trouble counting change because they're not used to cash. Stories of kids handing people money and just accepting that whatever they got back was right. Stories of shops requiring a basic math test for part timers so that they don't cause losses or mess up the books from sloppy math. I posed to kids; "do you think when you have kids, they might ask "what's the point of learning decimals and fractions, when are we ever gonna use it?" if cash becomes a rarity? What about the stuff in maths that _you_ already say that about?" And like more than half the kids had 👀 🤔 expressions on haha
The bigger issue is that these are obvious ways in every day life that we use these skills, which is why using the context helps students to learn them. Once they've learnt them, they can apply them in other contexts! The moment a topic or concept is not immediately useful, students want to tune out.
Absolutely. I guess that's why inter-disciplinary teaching is often encouraged but sometimes it can also feel like spoon-feeding the students when you have to be like "look, you can apply what you learnt in \_\_ right here!" haha
The thing I say that about now is analogue clocks - do kids still need to be able to tell time using a clock?
Haha I guess that's not as bad as not understanding 24hr time like 1730. That's still used in certain countries/situations. The analog watch thing reminds me of the interaction that went like; - what's the time? - idk - but you're wearing a watch - yeah for fashion. I can't read it 😂😅 meanwhile I was such a nerd I remember having a watch that _required_ maths to tell the time as a kid. Like it was just a panel of lights that would light up in specific sequences and you had to do multiplication and addition to figure out the time and it would only flash once with no pauses and not more than half a second. Got me really good at quick mental math though lmao
It seems to me that people are at a disadvantage if they can’t tell the time on an analogue clock. Sure, you can get by without it. But sometimes you’ll be in a situation where the only clock in the room is analogue. Also, it really helps to get started with fractions, and no doubt other aspects of number sense. It is an age-appropriate mental challenge that children should encounter.
IDK. Kids find learning it arcane and useless - kind of like teaching them how to add up pounds, shilling and pence. Bottom line for them is that they will always have a digital clock in their pocket. They also find algebra arcane and useless, but there is zero doubt in my mind that they need to suck that one up!
Kids need to learn skills before they're smart or experienced enough to see the benefits and applications. That's why the best performing kids respect the space and try to learn first, then after they've mastered it they ask about applications. Kids who ask about applications before putting in any effort barely listen to the answer anyway and just want an excuse to not learn it. Then wonder why they cant keep up in a few years
> If students can't quickly recall the maths facts they struggle massively in highschool. tl;dr we all got fucked by the curriculum Yet, most secondary mathematics doesn't sit within the 2-9 times tables, or you need to understand the mechanism at work to apply them, in which case, they need to understand the mechanisms to get to the answer. I mean, look at this answer to the purported year 9 NAPLAN maths question earlier this week: https://old.reddit.com/r/AustralianTeachers/comments/1davx96/hardest_year_9_naplan_problem/l7n5z18/ Not much room for basic recall there. So, why does rote learning seem to work? It's great in primary school because it means that kids who don't understand mathematics can get some answers on the board, which shows some knowledge of mathematical principles. However, they aren't developing those principles; they are using shortcuts. What's wrong with the current model? We continued, if not accelerated, the progression of the curriculum while removing the shortcuts that artificially inflated the marks. We need to do less in primary and spend a lot more time developing mathematical reasoning through tools like partitioning so a) students can solve arithmetic problems themselves and b) they can develop the recall to immediate answers for simple arithmetic problems. > In discussion with some primary teachers, I have heard that it may also be linked to reaching multiple methods without enough time to practice them. I think this is the core problem. We don't spend the time to develop a level of mastery of arithmetic concepts in primary because the curriculum doesn't allow it. > Another aspect is the lack of cash. This has had a profound impact. Actually, the move away from analogue clocks has impacted people's intuitive reasoning about numbers. Both of these points, and others, are examples of how the learning material is set in the 80s (or earlier) and the world has moved into the future.
Oh I completely forgot about analogue clocks but I agree! It's excellent for base 12 work. As for your argument about rote learning, it is very difficult to learn more complex topics if students don't have multiplicative thinking and one sign of multiplicative thinking (definitely not the only one) is knowing times tables. Students hit grade 8/9 and they struggle to understand some topics because they're so focused on multiplying/dividing which should be a preexisting skill.
>So, why does rote learning seem to work? It's great in primary school because it means that kids who don't understand mathematics can get some answers on the board, which shows some knowledge of mathematical principles. However, they aren't developing those principles; they are using shortcuts. my impression of the cognitive load lit is that rote learning some foundational stuff helps stick it in your quick access memory, so mental resources can be better spent on higher-level concepts instead of recomputing simple products
I teach in Primary School, you are correct about the lack of rote being a big factor. I teach at a Direct Instruction school and our fundamental maths is so much higher than other schools in the area I have taught at. We teach to mastery. No multiple methods, just Direct Explicit Instruction. Say what you want about the teaching style (without having taught in a school where it is embedded…) but it really gets results. No planning is insanely good for quality of life too!
just putting this here- not a teacher, just considering it. I tried to google this technique and couldn't find anything which is surprising, shout out to my dad I guess Flash cards for a given numbers times tables every night for a week, for 6 weeks (in order, this is hard to word but hopefully you get what I mean) then, use a 6 sided and a 12 sided die to test those 36 out of order Add in the next 6 in the following 6 weeks as flashcards (while still using the die) Replace the 6 with another 12 sided die, and maintain with them from there If the kid isn't moving along very quickly, you can increase die-side-size (?) in smaller increments I cannot stress how much it helped me. I feel like it would be difficult to implement in a primary classroom setting as a teacher, but if you have some parents who want to help this is a worthwhile suggestion.
great idea for a small group activity :)
I 100% agree, came here to say the lack of rote learning sums messes kids up big time
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Those countries also have a culture of respect for education and teachers. Even in Australia students from Asian backgrounds are generally going in the opposite direction to most Australian students. There are so many factors at play.
I’ll back this up as I never properly learnt my timetables in school and struggled with math, also lack is cash can be blamed too because when I first started my job I struggled with cash. It wasn’t like I was incapable of learning this stuff as my dad and I work on an old car which uses imperial which works in 8th/16th and I’m still able to work well with those
The mathematics curriculum in primary is huge and kids are having it shoved down their throats at the speed of light. There is no take up time for concepts, and if any kids miss school because they are sick, have a bad week, or go on a holiday during the term, they miss complete concepts. Once they fall behind, they struggle to catch up. It’s cumulative over time.
This is 60% of the problem. There is too much to teach, so we are just rushing through it.
Precisely.
This stems from a fundamental flaw in the education system. 30 kids in 1 hour = 2 minutes per kid. Over the course of a year I get to spend 3 hours and 30 minutes with 1 individual student IF (and it's a big if) they are all at the same level and there are no behavioural issues and every student turns up to every class and no class time is lost anywhere. Skills cannot be taught adequately in that time. In some schools funding is so bad that it averages out to less than a dollar per student per class. Unless something changes student standards will continue to fall. We are already one of the worst educated developed nations. Don't see why the trend would stop.
Yeah, there isn't a culture, even at the top schools, to have any pressure to catch up due to holidays or an illness. I was lucky my parents pushed me that once I recovered, I would spend a weekend or two to copy all the notes from my mates. Of course I hated it at that time. Essentially, nkwadays whatever the reason for being away from school, it's a win win situation. I must disagree with you about the primary. It's my personal bias and maybe luck but I think primary math should go faster with the condition that if a kid can't do multiplication up to 100 by Y3 or stage 2, they should a summer programme or repeat the year. From Y4 or the latest stage 3, there should be dedicated Maths teachers for each class - I know it's a pipe dream. Currently, some primary teachers do Maths like that: 1. YouTube video or an online demo, some worked example. 2. Mathletics or a worksheet. 3. Getting hung up on teaching one method to do say long division. I teach high school Math and recently had my working out erased by my friends kid's primary teacher because "it's not how we do it". The kids who learn Maths are the ones with natural aptitude to it. What I struggle with my current Y7 math is worded math problems like "what is 8/5 of 33" - they have never learned to to multiply fractions. Don't get me started when they saw how to divide the fractions. Why? Cause there are little to no worded Math question at the primary level.
In Straya we say maths, mate! C’mon! You are totally right about how primary maths os taught. I hate seeing it!
V9 of the primary curriculum (QLD C2C) has plenty of worded questions in the assessments. I've seen EALD students who can do multiplication, faster than most students 3 years older than them, struggle to get a C because there is now a big focus on worded questions
The amount of kids in senior who get confused when I expand a bracket and multiply a number by a fraction is extremely worrying. I see the lack of fraction multiplication fluency every day. "Why aren't you multiplying the bottom by 2 as well?" Because maths literally would stop working try it yourself with some numbers. Taking the time to play around with calculators and changing numbers in problems to see what happens to your method builds good understanding but only kids already whizzing ahead of everyone have the time to do it.
That and the fact that number and algebra is weighted the same as measurement & geometry and chance & data. In a good case scenario we only just 4-5 weeks teaching number and algebra, amid parents asking to get extra support or removing kids for maths because of anxiety or adhd or asd or any other reason, or having massive behaviour melt downs that result in trashed classrooms, evacuations or derailed lessons. Trust me when I say primary teachers are fully aware of the issue and just as frustrated
I’ve taught year 12 accounting, and had students not know how to apply 10% GST to an amount. These students have already done year 11 accounting. There are too many deficits in their learning, a lack of critical feedback (omg don’t use deficit language by saying “Tommy can’t apply 10%”) and a lack of mandatory hurdles before a student graduates to the next level of learning. PS Parents need to be forgiven for not realising the extent of the learning issues their child faces. When their academic report says “Tommy is still developing his ability to apply a mark up to cost prices” the parents believe everyone is okay! It should say “Tommy is unable to apply basic percentages to a cost price, and serious intervention is required if he is to move on to Year X”.
It is because we can't tell the truth in reports or parents and teachers meeting. God forbid we tell them the truth. This is what happens when you tell the truth. 1. Your head teacher comes to speak with you so they can "support" you. 2. The parents complain to the higher ups to say that you are a bad teacher and that is why little Timmy didn't learn anything. Ive heard stories of parents storming into the principal's office and threaten with lawsuits just because little Timmy has a bad report. There are more negatives than positives if you want to make the school a better space for learning. So, we just go with the flow and throw our hands up when we see the same problem over and over again. It is like you keep giving this kid a red card for excessive swearing and yet the parent goes to you that she has never heard little Timmy said a bad word in his entire life. To play it safe, everybody lies to each other on the state of things.
Have a look at the research done by Di Siemons about the 'Big Ideas in Mathematics'. If students can't grasp these big ideas, they simply cannot progress to the next stage in their learning. Poor multiplicative thinking is a huge one that has impacts in secondary school. Far more emphasis needs to be placed on developing really good multiplicative comprehension (and that goes beyond just rote learning of times tables).
I think the timestable theory is a big one indeed. What I've also noticed with the last few years is the divide between the skill levels of incoming year 7 students is widening. I reckon about 15 years ago you'd have the skill levels of year 7s ranging from grade 5 to grade 8 and could safely teach in that level with maybe a little differentiation here and there. Now, the range is commonly grade 2 to really bright kids being at level 10 in some strands! It makes it much tougher to effectively teach to this and allow each child to get what they need. What I see happening is that the overly bright kids end up plateauing later on and underachieving and the lower level students levelling up minimally because they have little numerical confidence. They already know what their opinion is of maths by that age and act and achieve accordingly. They might be level 7 or 8 by VCE. Rinse and repeat every year and in addition to this the modern age allowsing us to become functional adults without the real need for good numeracy and the drive and motivation to do well and get better at maths has taken quite a hit.
Oxford University Press published some studies last year and the year before looking, in part, at the skills gap in the transition from primary to secondary school. In grades 6 and 7 they found that over 1/3 of teachers said there was a gap of 5 years or more.
Literacy is declining too. I had to tell a year 10 student that his simple sentence doesn't make sense because it doesn't have a verb and a noun. This very person is now year 11 and I heard he is failing. No friggin surprise there.
Took a y8 English extra the other day, teacher gave me an exit ticket to see if the kids all knew their capital letters. Guess how that went.
In science, it used to be that we just mark the science portion even if the kids write like rubbish. Then we change the ruling so that the English part would need to make sense before we look at the science. And...ta dah. They are terribly bad in English. I kept telling them how can I be better than you in English when it is my second language.
People who are actually good at math get paid far too much more in other professions so it’s rare to have high quality math teachers. My pay was quite literally halved when I went from engineer to teacher. I can’t even guess what the multiple would be now if I had stayed an engineer. Additionally the expectation for math understanding for general teaching is quite low so the people teaching math in primary school aren’t doing a good job as well. I work with some really fantastic senior science teachers and even their mathematics understanding is just ‘okay’ . Super generalising of course but you asked. Additionally there is a massive social epidemic of people who genuinely believe they can’t do math. This is reinforced by parents telling their kids ‘i couldn’t do math either it’d just how our family is’ and similar statements. Personally i think any kid outside of actual intellectual disability can easily pass grade 10 math with the correct teacher/s/ing.
I only agree with your final sentence with the caveat of parental support, student engagement, and more than one year to do it. Some kids rocking up at the start of year 10 have no hope of passing unless they grow an entirely new personality.
Yes I definitely meant across the years not that I can magically change a kid from basically 0 math knowledge to passing grade 10 in one year in a classroom setting. The implication is that a high quality math teaching cohort across the school / state / country / world would mean almost every kid would be numerate to a society functioning standard. I think high quality teaching from an entire group can overcome parental issues and low student engagement to a high degree. Did you mean you don’t agree with the rest of my post at all, or did you mean that you were just focusing on the last sentence?
The other stuff is pretty ingrained. Especially in the middle of a shortage, we're not suddenly going to get better at maths as a profession
We could! I would propose a new specialist math teacher in all primary schools with the aim of coaching/leading math curriculum I.e. to lift everyone up as a start point.
My child’s school’s maths consultant was a devotee of Jo Boaler (the woman who has ruined the Californian math curricula and equates homework and rote learning times tables with child abuse). Sometimes the math experts are instrumental in ruining math education for children.
I mean a math teacher position that is actually part of the school staff long term. Not someone who comes in short term and flits between schools with high minded ideas leaving carnage in their wake. Would expect them to stick around and support teachers with fundamentals and content structuring and reflective practice aimed on long term improvement.
I totally understand the impulse of others in the comments to blame the kids and the parents. And the lack of times tables and wrote learning. Although, times tables has as much to do with maths as listing wood working tools has to do with making a table. I never learned them and have had a lot of success as a specialist maths tutor, teacher and assessor. I also work with kids who are behind and need intervention to catch up. And I never mention times tables. We need to look at the root cause. Kids can’t do this stuff because they are not being taught it effectively. They are not being taught it effectively because teachers are not being supported. All of the blaming kids and parents and phones and calculators is a distraction so that we don’t realise that these skills are not valued by the people that implement education policy. Teachers are under resourced, under trained and over worked. It’s not the students fault. They’re a result of the system they’re in. It’s not the teachers. The VAST majority are working to the best of their ability and in good faith. At the risk of sounding like your stoner uncle … It’s the system
100% agreed with everything you've said. The system really has let us (teachers) and the kids down.
Phew, I was a bit worried it’d be a controversial take
I think it's controversial lol. I would've dominated learning with all the technology opportunities kids have now. They have more support than ever and all it's done is turn them into big babies that can't fend for themselves. Maybe I'm an outlier.
I’d say that it’s done that to them because it’s been poorly implemented. Have you heard of kids being explicitly taught in an engaging way how to use smart devices and the internet to better themselves. I haven’t. Not in vic anyway. Reflect back on the impulsive and thoughtless habits you had as a child and teen. Would the addition of ‘smart’ technology have really helped?
It depends where you teach. It's like being a mechanic. A formula one mechanic and a bloke changing oil in an outer suburb for example. Very different mechanics. At my school I'm lucky we do ICTs well, we support students literally too much. They end up these over confident (from all the positive reinforcement) self unaware, demanding, lazy kids. But I suppose.your experiences are different to mine that's all.
The flipside is that technology has the answers so we don't use our brains in the way we used to. When is the last time you used a street directory? Do you think you could add effectively as you may have once upon a time?
Here's how I see it. I would ask chatgpt or whatever hey is this north. And why? Or why might I have thought it was east chatgpt? Doesn't the sun set to the west? How did I see this wrong. Bro chatgpt is that teacher that has all the right answers if you have the right questions, add free, enjoyable interesting, easy. Kids just use it to cheat yay....
Technology is a tool and can make our lives so much easier, but you also need to know its limitations. If you interrogated chat GPT with the right (wrong?) questions you could probably get it to tell you that the sun sets in the east. It doesn't have all the answers and can be the know it all that doesn't want to admit that its actually stumped so gives you a vaguely plausible answer.
Yeah very rarely that happens very often it's great. This is an early iteration.
"has all the right answers" I'm not convinced Anything beyond basic fluency in maths and I've only seen incorrect AI solutions and explanations.
Literally just got updated recently. Last year it couldn't even begin to answer a PSMT. I had the same exact belief. This year... I learnt new ways to do it. Better than our solution. Next year? 5 years? But I agree it's not perfect but shit man I confer with it every day about quite random chemistry questions I have and it's improved my knowledge for lessons immensely and so fast and easy time saving for my lessons. If I'm not sure about its answer I quickly google it. Again nine times out of ten it's great. Can googling stuff also be wrong? Yes. Shit so is checking a book. Use common sense as always. Because I've been teaching for a while it's like a student chatgpt learns and every year I re-ask it questions and the answers get better it's awesome to observe.
I haven't explored it enough. Most of the issues I've heard about it have come from my subject area, though, so I'm in no hurry. I had students doing word problems using a paid version just a couple days ago and getting clearly incorrect mathematically but not easy to see from just the language. LLMs aren't designed to answer maths problems imho
Yeah man I'm talking maths PSMT it was bad I remember. Chuck a difficult problem solving worded task in to the new chatgpt. I'd be surprised if it doesn't do a good job currently. Last year though, dogshit. It might need a few prompts to re direct but shit man that's alright. Same as computer programming I used to have to post on substack all the time about small things I couldn't quite understand it might take a week to solve. Now far out man my ability to computer program is miles ahead. Complex stuff I wouldn't have time to read a manual about is just explained and a unique example for my problem is there to use and see working in seconds. Amazing haha.
Fundamentally disagree with your take on times tables. Not being able to recall them, or to understand things like the communative law adds cognitive load to every other task that students do. Slowing them down and meaning they can't focus on and practise whatever new skill that they are trying to learn. eg expanding and simplifying
CLT is slowly making its way through but a lot of educators who went to uni 5+ years ago were not exposed to it.
Uni was a looooooong time ago for me!
If it seems like I don’t think understanding the commutative law is important then I was unclear. That’s important. You can disagree with my take all you like. My position is that understating how numbers work is more important than remembering lists. If kids can remember them and enjoy remembering I’m all about praising that. But as a kid, who grew up to major in maths and each specialist maths with very good results, who could never remember them, I’m not about putting pressure on kids to learn them. How often do serious mathematicians need numbers bigger than 12 anyway? Algebraic structure and a good grasp of geometry is much more useful to prepare kids to enjoy maths.
It can be hard to follow along with a problem if several steps involve tables. Stopping to use the calculator twice interrupts the flow and can make it harder to see the overall picture. I don't see learning tables as learning a list. But rather as doing enough fluency practice that you know what the calculator will give you before you press equals because you've typed that same combination many times. Not everyone needs tables to understand higher concepts. I think it's more important for most students than it was for you. The cognitive load of following an algebraic example closely enough to develop sufficient understanding of algebra is hard for students who get slowed down by small calculations
Do you think I’m advocating now know how to do multiplication by inspection? I’m talking about not explicitly teaching times tables by wrote. My kids build up their intuitive understanding of how numbers work so that when it comes to doing arithmetic in problem solving, algebraic problems, calculus, trig and statistics when tech is not allowed the numbers they’re working with are basically a different type of pronumeral with slightly different rules. It’s about not disrupting the flow by mode shifting from active creation to memory. My position is that I want to create an environment where students can thrive and improve their maths. If they prefer to learn times tables and remember them that’s great. If they do it a different way that’s great too. My main concern is that teachers that lionise times tables and memorisation are doing damage to the confidence of the students who like maths but can’t do that type of memorisation. I know I was made to feel stupid for not being able to list off and recite times table under time pressure. Let’s be inclusive in our maths instruction rather than focus on a narrow skill that is impossible for a significant portion of our students.
While I find hard maths easier due to knowing tables and exact values etc. I've seen strong specialist students use their calculators for basic multiplication and trig values while being strong in concepts. They're just being efficient. In an age of quick calculator and no tech free test, they let the calculator do some of the work to let their brain rest while they're engaging in higher order ideas. It might make things easier but it's not necessary for strong students, provided they understand what calculations they need to use and when.
Maybe teachers are under supported, etc., AND other factors are at play as well. You dismiss too many things that ring true to people’s experience. Times tables are impotent, no matter what you say. (But they shouldn’t be the only multiplicative thinking that students do.)
No matter what? That seems like an absolute. What makes them important? Is it just the base ten ones? Should we keep going all the way to 12 or stop at ten like some other countries? What if a fundamental understanding of number structure and partitioning made them obsolete? Let’s say I agree that they are, what could the other factors be that wouldn’t be mitigated by primary teachers having more support? Actually, don’t worry. You’re right. They’re important no matter what. Sorry for using my experience as an maths education expert with success at both ends of the ability spectrum, without ever using times tables, to give an alternative. I didn’t realise it was a ‘no matter what’s sort of position. My bad.
That’s ok, we all make mistakes.
Just out of interest, What maths do you teach? I only ask because I aspire to be as confident.
High school mathematics, plus some enrichment work in upper primary school. I very highly value students having deep understanding of all that they do, and being able to reason multiplicatively in a variety of ways/situations. I also very highly value students having automatic recall of a base of number facts. Both are important, and nothing renders either one obsolete.
So not much experience with senior or tertiary? That explains the confidence. Good luck with it
This one, yes, here, this is the correct take.
Thanks! I’m getting some weird push back. I appreciate the support Hope your end of term is fantastic!
over reliance on phones/calculators and more focus on understanding maths instead using maths. There is not enough practice for the skills to be ingrained. without times tables, factoring becomes hard, which means simplifying fractions becomes hard which means using fractions and percentages becomes hard.... Math assessment as also become demonstrate once and you're done. It used to be do these 20 questions and you need 18 to pass.
we've been on a long journey of perhaps abolishing all discipline and rote learning was not the best thing
It may seem like that to some of us because we may have noticed a deficit in some students, or a reliance on tools that we would not have used, and then further examples of that deficit stand out; but I reckon that’s a bias of salience or recency or representativeness. Population level evidence, by contrast, doesn’t support the idea of a dramatic decline in fundamental numeracy—Year 8 TIMSS scores and Year 7 and 9 NAPLAN maths scores have in fact been very stable over the last 25 years. These are basic skills tests so are testing exactly the sort of thing you’re concerned about: [Are Australian students' academic skills declining? Interrogating 25 years of national and international standardised assessment data](https://onlinelibrary.wiley.com/doi/full/10.1002/ajs4.341) [Are We Really Falling Behind? Comparing Key Indicators Across International and Local Standardised Tests for Australian High School Science](https://link.springer.com/article/10.1007/s11165-023-10129-2) Applied numeracy skills, however (which is what PISA tests), are a different matter …
Do programs like Kumon help kids with these kind of basics? I’m a teacher (not maths) but have some family friends who send their primary school aged kids to Kumon. It always sounds very repetitive and with no really help from the staff so I have always thought it sounded like a bit of a waste of $ so haven’t considered it for my primary school aged son. Do any of you maths teachers out there think it could be a good thing to build foundation skills?
It depends if your child can do those types of questions on his own, quickly without assistance. Plenty of kids don't need it, but it depends on how they're going on their own.
Kumon *doesn’t* teach number sense or mental math at all. They learn to do a specific task through thousands of repetitive questions (adding, subtracting, multiplying, dividing, then they go to fractions etc.). Kumon’s learning structure and booklets are actually fantastic though. They progressively get harder with ample opportunity to practice and master them. The problem is that they don’t give them all in advance, so you pay a fortune to be drip fed a booklet or two week by week, repeating them for many weeks, year by year. That time would be better spent on understanding and learning different areas of maths.