Make 'Em Think Maths
Welcome to Make 'Em Think Maths. On this website you will find ideas for teaching Mathematics with a focus on conceptual understanding. Time is precious, so I make short informative animations and stills for teachers.
I don't want this website to be just a bank of pdfs and powerpoint resources. I think the best resource we have is our own resourcefulness. I hope this site gives you ideas for you to run with and therefore enhance the learning of others.
Follow on Twitter: @mcguirea499
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Principles and Mantra to teach Mathematics by.
- Concept > Procedure
- Give students agency
- Make the time to remember
- Teach them the next thing
- Make 'em think!
2. Give students agency
Giving the students agency within the context of what they are learning, brings them 'closer' to the Mathematics. Now their schema is more established, let them explore. Widen the path. I am not saying let them have free reign, but think about how you can loosen up the constraints to allow exploration. Some would say this a great form of differentiation.
3. Make the time to remember
Retrieval practice is the act of recalling what you have previously studied. It’s a way of getting information out of your long-term memory. The act of doing this, strengthens your memory of the thing you recalled for future retrieval. Sounds like revision? It’s not, it’s learning strategy. A very important learning strategy.
4. Teach them the next thing
Find out what they know and teach accordingly. If you find yourself scaffolding so much that the maths is just a set of rules to memorise, it is probably because they are not ready for it. If I tried to learn about astrogeology at my current level of understanding, I would have no chance! I need to learn the next thing. I need to build schema and make connections to the things I already know. As Mark McCourt talks about in his book Teaching For Mastery, we put our children on a conveyor belt based on their age, not their current stage of understanding. Let's take the labels off and find out where they are and teach from there.
Latest teaching ideas:
Fraction Sense - Ratio Table - Fractions of Amounts
Using the ratio table, double number line and bars to develop fraction sense. Fractions of amounts.
Making Links With Trigonometry
Teaching Trigonometry for Understanding - Part 1
SOH CAH TOA is a trick. A necessary trick for last minute teaching of Trigonometry. What does it look like if we try and teach it for understanding? Trigonometry needs to be visited in year 9. That should give us enough time to teach it properly, surely?
What is the same and what is different?
Additive vs multiplicative relationships with exponents
With number first?
Equivalent Fractions Linking to Multiplication
Using the area model to explore equivalent fractions and how the same representation can be used to conceptualise the multiplication of fractions.
Expanding Brackets: exploring the distributive law
I have been planning how I would teach expanding brackets to students who haven't seen it before. Do teachers focus enough on the distributive law? I feel, most students have a sense of this in their mathematical 'tool bag' and from prior learning. Why not tap in to it? Make 'em LINK!
In this clip you will see how I have tried to embrace a connectionist mindset in my planning. Thanks to Chris McGrane's Mathematical Tasks book for making me reflect on this.
Thinking about Standard Form
Ideas for learning Standard Form.
I try to borrow knowledge of powers of 10 and also students work on indices - especially reciprocals.
Using the Gattegno chart to construct numbers and then multiplying/dividing by powers of 10 can really help pupils see what is going on.
Substitution Memory Game
Low starting point- high ceiling task. An excellent way to practice algebraic notation whilst learning substitution.
The gives pupils a sense of agency. They have the opportunity to own the Mathematics with tasks like this.
What equations can you make?
Can you see... y = 1 + 3
x + y = 5z
(5+1)/3 = z
The list is endless.
What equations can you make? Display students work and get others to try and find them.
Deeper understanding task: Build your own picture!