Teachers' capability to teach maths a concern - ERO
These comments are in reference to the following interview on RNZ on 6 July 2021
Teachers need Maths Support
There is no doubt that teacher capability to teach mathematics is a very complex issue and teachers are doing their best and there is no single silver bullet to fix it. But something needs to be done to support teachers, many of whom themselves will undoubtedly have suffered from maths anxiety themselves. Yes, it's a real thing.
Learning Advisors
I remember the existence of Learning Advisors who were of tremendous support to primary teachers in mathematics, science and technology up until about 2010-11 when they were disbanded. These advisors took two years off teaching to help other teachers. In Christchurch they were based at the old Christchurch Teachers' College. Bringing them back would be a huge step in the right direction because these advisors went into each teacher's classroom environment and could provide direct, relevant and appropriate subject support as needed. Megan Clune is right that this potentially takes "quality" teachers out of the classroom but the long term benefits of having more teachers becoming confident and competent in their capability in maths would outweigh this.
How Often is Maths Being Scheduled
As a specialist mathematics tutor I ask my students every week, what have you been doing in maths at school this past week? There are of course a range of answers but more and more I hear for primary schools students, "We didn't do any maths this week." I have found that not every school does maths regularly. There are some primary schools who don't do maths for an entire term. For example, it might be the school production term so maths is sacrificed for an entire 10 weeks for "production practice". I think this is unacceptable as maths needs to be constantly practiced to avvoid slippage in skill level. Another regular response is "We did worksheets" (which includes paper worksheets as well as online maths games like Prodigy and Maths Buddy etc). In the RNZ interview, Megan Clune did mention how often worksheets are given (without direct instruction) and I have to agree that teachers are snowed under with other administration and tasks that makes them time poor for thorough preparation of classroom lesson plans and exhausted to even think about additional personal development.
Briar Lipson was on Q&A with Jack Tane a short time ago and I loved it when she said "so on a Tuesday afternoon when it is raining and you can't play sport as planned, teachers should take the opportunity to facilitate practicing basic facts" and I thought "Exactly, rather than singing songs and eating chocolate cake" which are important celebratory things but whenever you have unexpected time why not use it to rehearse your basic facts skills. It doesn't have to be boring it can be in the form of a game or singing to find the rhyme and rhyme of the times tables.
Too Much Content in the Curriculum
One secondary school I know has a subject called STEM which is Science, Technology, Engineering and Mathematics all rolled into one for their junior (Year 9 and 10) students. I think that this is in principal an excellent idea because maths should always be taught in connection with applications. Maths doesn't exist for its own sake. Unfortunately, this set up means that at least three subjects are taking the "time allocation" of what would have been time allocated just for maths and in my opinion doesn't provide enough maths time for practice, consolidation and mastery. I think it is a clear indicator that there is far too much in the curriculum. More stuff keeps being added and nothing is being taken out. We have ended up with a little bit of everything and not enough time for mastery of any! And yet I believe a solid grounding in maths facilitates easier learning of science and technology subjects.
Negative Maths Attitudes
In the RNZ article Megan Clune also mention teacher attitudes to maths. I have witnessed on several occasions primary school teachers saying to their class, "if you are good we won't do maths today we will do something you will like" (meaning sport, music or art). These types of comments send out the wrong message to students. I say to my students, "You don't have to love maths, you just have to be able to do it!" Learning maths is like learning a musical instrument and practice enables a satisfactory performance.
Teaching Methods
I was surprised that The Numeracy Project (introduced as new maths teaching methods around 2002) was not mentioned in the RNZ interview. I thought the ideas behind the teaching methods of the Numeracy project were great but that is because I already understand maths. What actually happened was that students were required to show several different methods to do one calculation and this is what was confusing for them. At at parent teacher interview for my own son, I was told my boy could only do one method for addition. "You only need one method!"
The Column Method is now not taught in schooIs until the intermediate years but I am a huge fan of this method (now called 'algorithm' method) for addition, subtraction and multiplication. This is because it doesn't matter how big the numbers are, it always works. It's not just a method for 1 and 2 digit number calculations. Students who start with me who are in Year 6 and seem almost paralyzed by any math calculation are able to not only add or subtract numbers up to 100 but numbers much much bigger. Column sets students up for success and then they are on their way. They can get the right answer and they know it is the right answer. That's the confidence boost that gets them excited about yes I can do this! Once they have mastered this then I introduce the other strategies and with their increased confidence they then are able to better grasp alternative methods.
I now teach short division in preference to long division because students get lost in the process of the division, multiplication and subtraction calculations that are all part of a division calculation. Students who come to me baffled and confused by long division are soon set on a clear path when I show them the short division layout (which is of course the same maths) but it is a less confusing format.
Group Work
There is greater emphasis by the Ministry of Education on focusing on getting students to understand the concepts of maths and so encourage teachers to facilitate maths concepts by getting students into groups to discuss and work out the maths themselves. This is also a way off managing mixed ability students since more able students can in theory assist less-able student. Remember that as a tutor I am mostly dealing with students who are struggling with maths at school. I use a combination of direct and indirect teaching methods depending on each individual student but I have found that more direct instruction is more successful, especially for shyer quiet students who have personality types where group work is daunting for them and sometimes provides an additional level of anxiety. It takes a lot of time to "discover" or "re-discover" how maths works, and frankly with the amount of content to be covered across all curriculum areas, direct instruction is better for the masses and the proof can be for extending the students with higher aptitude and faster mental processing capability. If students insist on always knowing the "why' when learning maths then progress will be very slow. I tell my students you will find out in later years as you advance and as all the topics in maths begin to connect to become a big bucket of inter-related problem solving tools. I have sometimes said to students who are blocked by needing to know why, "for now just trust the maths".
Personal Abacus
Something I became aware of recently was that students aren't considered to pass curriculum level one maths (Year 1 and 2 students) if they use their fingers to count. I was shocked at this. Quite frankly I still do this occasionally myself (particularly for time) and I have a maths degree! The students become secretive that they use their fingers and hide their hands under the desk (almost in shame) to work out the answer in the hope that they won't be seen using their "personal abacus". What matters is that they get the right answer! I tell my students, "Your fingers are the best digits you have so use them". Of course, as they progress they will move to not using their fingers and some will progress faster than others but they shouldn't "fail" or be berated because they need the use of an abacus to support their counting.
Visual Thinkers
Another aspects of modern maths learning is that students are encouraged to “imagine" numbers in their heads and do a lot of mental arithmetic. This is a very good skill to have but what is wrong with pencil and paper. Some students can do calculations quicker in their heads than on paper but others can't. So both should be perfectly acceptable. Not everyone is is visual learner, others are auditory while others are kinaesthetic (need physical objects for concept recognition). The thing that matters is they get the right answer and they know it is the right answer.
