Category Archives: math education
New Zealand Graduating Teacher Standard 1.a
Graduating Teachers have content knowledge appropriate to the learners and learning areas of their programme.
It was just a simple maths warm up called ‘guess my number.’ It’s kind of like hangman but for maths.
Now I’m sure you are rolling your eyeballs.
But the thing is this game is great for getting kids to use place value so long as you can make the thinking visible.
So we start with the learning.
WALHT: use place value to guess a 3 digit number.
I use 3 digits because that’s about where my year 1/2 learners are at. But you can go down to two digit numbers to start with or up to 5 or 6 digits depending on what your students learning needs are.
The success criteria is simple students will be able to explain how they guessed the number using place value. This means even mistakes are opportunities for learning if you ask the right questions.
I write 3 spaces and the students start guessing the number and put ticks and crosses beside the guess according to whether each number has a correct answer. So if a student guesses 124, I will tick 1 and 4 if the ‘answer’ is 194. Nine gets an X.
I will always give a ‘tick’ for one number on the first guess to start the students off.
From the second guess I will start asking questions.
How did you know to pick that number? What digits have ticks? What do you think would be a better guess for next time (if a student makes a guess that hasn’t used place value)? What digits do you think will have ticks?
A student wins when they are able to explain how the guessed all three places (which I point out is the success criteria for the game before we start playing).
What was amazing wasn’t how quickly students started using place value to make their guesses, but how they chose to adapt the game.
At the end of one warm up a student commented that he wanted me to record a plus or minus sign instead of ticks and crosses. So for the next lesson I use his suggestion and away we went. The students quickly figured out that using plus and minus signs meant the game was a lot easier because the symbols told them whether to pick a number greater than or less than the previous guess. So not only were the students were not only using the language of maths they had stumbled upon a key concept of probability, chance = favourable outcomes/total possible outcomes, and were now using it to improve their odds! I hadn’t even considered using plus or minus as a way to record answer which showes how agile children’s minds are when the right questions are asked.
I was dumbstruck that a simple warm up yielded such great learning moments.
The students have now decided guess my number is too easy and want to guess 4 digit numbers.
Who am I to argue?
Teaching Experience 1 is all over bar submitting the paperwork (and dear god is there a lot of paperwork).The last few weeks in particular have certainly given me a lot to reflect back on as I went from an observer and small group teaching to taking responsibility for planning and teaching 4 classes a unit on probability over the last few weeks. I also taught some algebra, fitness and a Te Reo class. Despite my initial jitters I’m thankful that my associate let me pretty much have free reign over the classes for three weeks. I doubt that I would have learned nearly as much if I had done the minimum of 5 days of full control. Certainly having an opportunity to do some unit planning was a highly useful exercise.
I also valued teaching in a school that not only was highly ICT friendly but also had specialist teaching. Not many primary teacher trainees (or indeed teachers) get the opportunity to develop skills in a specific subject area, maths in my case, and I had the opportunity to do so relatively early in my career. Hopefully there’s a school out there which would value someone with some extra maths teaching experience enough to give me a job.
Effective classroom management is essential - You can have the greatest lesson in the world planned but if your classroom management isn’t up to snuff then it doesn’t matter. It’s amazing how gust a few tweaks in classroom management can make the difference between a good lesson and a great lesson. But on the other hand, a few missteps can turn a good lesson into a disaster. I’ve ended up at both ends of the spectrum, and did need to be reminded to actually use all those classroom management techniques I’ve written about.
Keep it Simple and Succeed – There were times when I had far too much going on the classroom to manage it effectively. This is undoubtedly because I’m still stuck in the beginning teacher mindset of ZOMG 45 minutes how on earth am I going to fill up that time? Rather than realizing that by the time the students arrive, get settled and pack up, they’ve really only got about 35 minutes of proper learning time and ZOMG where did the time go? To that end, I need to work on making sure groups are better aware of what they are doing and having some relevant activities set up for students who do finish early. I also need to not bite off more than I can chew during my lessons.
In terms of planning I am generally happy with the overall concept and also using evidence to develop the unit of work. I have some work to do on developing success criteria and making those known to the students. While I am reasonably happy with my planning, my execution is still not particularly good. My major problem areas at the moment are classroom management and time management. I’ve got a good repository of management techniques I could use but need to develop my own style for which ones I actually use. Time management will be even more important in my next placement where I will not have a bell every 45 minutes to remind me that it is time to change lessons.
Despite my poor performance in some areas, I’m so stoked to have had such a fantastic placement at such an awesome school with such a great associate teacher. I’ve been recommending my school to one and all whether they have kids or are in need of a placement for teaching experience.
Right now I’m trying to summon some enthusiasm for lecturers and assignments now the ‘fun’ part of the diploma is over for the next few months and I’m back to the drudgery of readings, assessments and exams! Oh my!
New Zealand Graduating Teacher Standard 1.b
Graduating teachers have pedagogical content knowledge appropriate to the learners and learning areas of their programme.
Maths has changed a lot since I left school. When I was in primary school maths generally revolved around teachers modelling an equation and then the students were given a whole bunch of problems to solve using the equation. There was also a lot of ‘skill and drill’ which must have been effective because many decades later I find myself transported back to my primary school maths class reciting the timetables. I loved the subject, but I knew a lot of kids had an unhappy experience and that numbers were just a mystery.
Nearly two decades later I’m back in primary school where the emphasis is more on teaching numeracy. Despite many people’s hatred of the subject, maths is used all over the place. When we go shopping and see 20% of a shirt, what happens if we buy two shirts, is it 40% off? In baking people often double or half a recipe depending on their needs. Sports uses all sorts of fractions all over the place and the old adage those who don’t understand compound interest are destined to pay it, partly explains the prevalence of loan sharks in areas of low education and consequently low income.
So I get the importance of making the connection between ‘every day maths’ and what happens inside the classroom.
Getting kids to use materials and images to explore the principles taught BEFORE getting them to writing out the equations. There’s also a lot more emphasis on being able to use different strategies and formulas to find formulas,
The group I have been working with in a maths class have been learning about fractions. Last week they were working on ordering fraction and this week they are using fractions of a set using addition. eg. 2/3 of 18 = 6+6= 12. I’ve been using the Hungry birds which we decided were jelly babies, but the point was the same. The kids took to the lesson where we were using materials and imaging quite quickly and in fact were complaining that it was too easy. “Woohoo!” I thought to myself. Time to move on to using number properties in the afternoon session.
Now the students at the school scamper off to other classes before coming back to see me in math in the afternoon
The group and I met again in the afternoon and I was keen to get started on using number properties. By the end of the lesson I was despondent to find over the space of a few hours, that for a few students the bottom fell out and were back to square one. Worse than that, one of them had forgotten what the numerator and denominator’s role in fractions.
Things I will do differently next time.
Done more of a recap of the previous lesson, especially jogging the memory of some students about the parts of fraction.
Getting kids to practice writing down what they see when they are in the using materials section.
Any other suggestions?
The first week of first trimester has seen my workload triple. Instead of taking one course on theorists I was already familiar with, I am now taking three courses: numeracy, literacy and teaching strategies. Of the three courses teaching strategy is the one causing me the least headaches (I’ve already had 4 years in a classroom as language teacher in Asia) while the numeracy paper is definitely causing the most anxiety. I find myself waking up in the middle of the night thinking about math!
Oddly my mathphobia wasn’t because I hated math at school. In fact the opposite is true, I enjoyed and did well in math up until about year 12 /13. What’s caused my anxiety is that the teaching of math has changed considerably from the skill and drill style I excelled in during my schooling years. The focus now is on to getting learners to use strategies and build on their prior knowledge in order to solve math problems, rather than just following formulas taught to us up the front.
I think this style of teaching is exciting because I can see how it would get more kids turned onto to math by getting them to think about how they arrive at a concept rather than just blindly following a model that may (or more likely may not) have any meaning to them. But it has also challenged my own perceptions of math and made me realize that I have huge gaps in my own numeracy skills. Doing the old-style long division seems like a breeze in comparison to the multiple pathways that students could employ to get at their answers. Nevertheless, I can see how this new method might take the terror out of math for some students and deepen their understanding of numbers.
It has been a tough week to come up to speed on the New Zealand Curriculum, English Language Learning Progressions, National Standards and the Numeracy Development Project. Of the documents that I’ve been speed reading, the Numeracy Development Project documents are the ones that I am finding the most stimulating. However I’m not sure where exactly National Standards fit into the mix of documents, other than to say I feel for all the year 1-4 teachers who are having to do assessment based on http://nzcurriculum.tki.org.nz/National-Standards/Reading-and-writing-standards/The-standards“>when a student starts school rather than at the end of the year.*
So what I have learned this week?
Prioritize – There are only so many hours in a day and only so many concepts I can wrap my head around in one go. At the moment I am focused on getting my assignments done and grasping as much of the course content as I can. Then I’ll use the holidays to catch up on the stuff I missed.
Do or do not, there is no try – Yoda was right, there is no try. This week has flown by in a flurry of jargon, acronyms and concepts. I’ve read a lot of words but don’t feel like I’ve absorbed much meaning but that’s because I spent half the week trying to understand and feeling like I was failing miserably. Once I attempted my assignments and found I was able to bang out half of them in the space of a few hours. I’ve discovered that the best way to get a grasp on all these readings is to put them into practice.
Put away your cape – Perhaps one of the biggest pressures student teachers feel is that they have to be super teacher from day 1. The large number of documents that I’ve had to absorb this week have upped that pressure a further notch. But then I remembered the wise words of one of my friends who freely admitted that his first few years of teaching weren’t his best work and he needed time to work out his own style of teaching. Being bad when you start is normal, not being open to improving is the problem whether you are a newbie student teacher or an educator with decades of experience.
This week more than any week so far has made me feel like I am practising for real life. I know that out in the ‘real world’ there’s always going to be something for me to read and reflect on and more importantly there are going to be demands placed on my time and my students’ time. Learning the ins and outs of what the State requires from our education system and then finding ways to make it work in a classroom setting seem as daunting as a half-marathon course at the start of the race. But I’ve made it across that finish line, and I’m sure I’ll make it across the next one.
I was also reminded how quickly education changes. While some would say this is a bad thing, education by its very nature is in a constant state of reform. New ideas, new students and new technology mean that teachers are constantly having to change the way they practice their craft and that has implications for the sector as a whole. Nevertheless, I would love the Ministry of Education to stop churning out documents for a couple of years so that I can get a handle on things.
We’ve had the slow food movement, anyone up for a slow education one ? I promise there will be no capes
*New Zealand students generally start school on their fifth birthday rather than at the start of a school year or term.