**Make heavy use of the pre-prepared questions and solutions from the Mathematics Enhancement Programme, to quickly prep lessons**

“Don’t try to reinvent the wheel!”

“Look on TES!”

Two oft spoken quotes that aren’t very helpful. There are limitless maths resources out there, some terrible, some will change your life.

As a maths teacher much of your lessons must necessarily revolve around setting the students questions to practice, and then telling them the answers. Okay, there are many variants on this model, but practice certainly sits at the core of strong learning.

Creating all your own problems, and solving them, and differentiating them, enough to keep 30 students engaged for 30-40 minutes of practice per lesson, is mentally exhausting. Don’t try to reinvent the wheel; many people have already produced exactly what you need. But… where is this wheel, what does it look like? TES is huge, and mostly filled with what you don’t need.

I want to show you the wheel.

**Voila, the Wheel:**

One resource, which will potentially change your life.

The Mathematics Enhancement Programme (**MEP**), produced by the Centre for Innovation in Mathematics (CIMT) back in 1995.

You’ll probably hear a lot of talk about the Standards Units during the SI. They really are great resources, and they’ll get you thinking about maths in new ways, but they have two major caveats that may not be mentioned:

- They are far from exhaustive – They are about deepening
**understanding**of core mathematical ideas, not covering curriculum content (which is your first and foremost responsibility) - They are utterly inaccessible to pupils who haven’t first been taught the basics in a more traditional manner

So how do you teach those basic concepts? **Enter, the MEP!**

The MEP is an exhaustive repository of the best traditional teaching resources I have seen. There is far more content than can be delivered, so I recommend focussing on **the ‘Pupil Practice Book’** for each module.

Exceptionally well structured sequences of work, that will help *you* as a new teacher understand how students can set out their working. Each sub-topic in the practice book includes the facts and processes they need to understand, followed by 2-4 worked examples, followed by well-structured rote practice questions, followed by more interesting worded questions, followed ultimately by more complex relational questions.

If that weren’t enough, look at the other resources for each module to find mental tests you can use as starters, what they call ‘Activities’, which are often investigative resources for deepening understanding, extra practice questions if needed, and diagnostic tests to assess their progress. There’s even a ‘Teacher Notes’ resource for each module, that usually gives some information on the **history** of the mathematics, and a little **real world context**, or some well written **maths-lovin’ paragraphs** that you can throw up on the board to help inspire your students.

Find them at one of these two links (use whichever you find easier to navigate):

http://www.tes.co.uk/article.aspx?storyCode=6075946

http://www.cimt.plymouth.ac.uk/projects/mep/default.htm

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“Creating all your own problems, and solving them, and differentiating them, enough to keep 30 students engaged for 30-40 minutes of practice per lesson, is mentally exhausting”…..this is also a very boring way of students to learn. Students need to understand and be able to apply the maths, not just be able to repeat a drill. Standards box is an amazing resource as is maths4life and one of this best in http://www.nrich.maths.org

‘Repeating a drill’ is a very loaded phrase, and it means different things to different people. Writing out times tables again and again, is arguably a drill; there is no problem solving element to it. It can be boring, yet also it could be an essential part of a student memorising important mathematical facts. ‘Understanding’ multiplication is not nearly so important as knowing multiplication facts by heart, if what you need to do is simply multiply numbers. Both are important to a person’s mathematical education.

Solving problems is not a drill, it’s applying a new process that’s been learnt to familiar contexts, so as to build mathematical fluency and enable the process to become automatic. Once it becomes automatic, it places 0 load on working memory, leaving available all of the brain’s processing power to learn new, higher-order ideas that incorporate the lower-level process. Both Willingham (http://www.amazon.co.uk/Why-Dont-Students-Like-School/dp/047059196X) (Willingham, D., 2002. Inflexible Knowledge: The First Step to Expertise. American Educator, Winter Issue, pp.8-19 — http://www.aft.org/newspubs/periodicals/ae/winter2002/willingham.cfm) and Skemp (http://mathmamawrites.blogspot.co.uk/2012/07/book-psychology-of-learning-mathematics.html) make this clear. Willingham also notes that problem solving *is* fun: every brain is neurologically predisposed to enjoy solving problems. Similarly, people love ‘getting things right’. Mathematics is uniquely placed to offer the opportunity for people to ‘get things right’, yet many new teachers are made to feel guilty for showing students how to solve a problem (such as expanding a bracket), and then simply giving them an almost identical problem whose solution they are to reproduce, without being placed immediately in a new context (e.g. find the area of a rectangle, with sides 2 and x+5). Yet this unfair on the kids. We’re not only denying them the opportunity to see that they’ve just learnt something, but also failing to recognise the cognitive demand placed on ‘simple’ reproduction of a demonstrated process. Both Solity (http://www.amazon.co.uk/Michel-Thomas-The-Learning-Revolution/dp/0340928336) and Engelmann (http://www.amazon.co.uk/Theory-Instruction-Applications-Siegfried-Engelmann/dp/1880183803) state that varied context is necessary for generalisation and transferability, but it must come *after* application within familiar context.

Resources such as nRich, Maths4Life and the Standards Units are excellent, but they’re excellent in a particular context which is rarely made clear to new maths teachers. As suggested in your post, new teachers are told that ‘doing 10 questions’ is dull, they’re told it doesn’t promote learning, doesn’t promote relational understanding, and instead they should use more complex problems such as those listed above. The idea that ‘doing lots of questions is dull’ was disproved for me in my second week of teaching. At the end of the first, my subject mentor sat me down and told me that to *us*, as experts, it may seem dull, but actually the kids will do pages and pages of questions, quietly, loving the feeling of getting it right. I didn’t believe her until I saw the book of one difficult student in a low-level group the following week, in which he’d successfully answered three pages worth of questions. Who are we to now take that success away from him, and say that what he’s learnt *isn’t* good enough, or wasn’t sufficiently challenging? He’s learnt something, and he enjoyed the feeling of success, that’s step 1. The more complex understanding and problem solving skills come later. By contrast, I hear story after story from new teachers, including my own experience, where we’ve jumped too quickly into high-level thinking problems like those you suggest, and none but the very best in the top sets are able to come anywhere close to accessing the content. For the rest, their learning simply stagnates. They feel frustrated. They grow to hate maths. They start to believe they can’t do maths, and the success of the minority around them reaffirms that it is indeed *they* who are to blame, rather than the teacher who has not given them time to practise, time to learn, as this is what the teacher was told is good practice.

Fluency must first be developed. Once it is, and students can easily, and comfortably handle simple mathematical processes, *then* they can be introduced to more complex problems, in an effort to build that relational understanding.