The Elephant in the classroom Jo Boaler Staff reflections - Thoughts

This is my reflection after reading the introduction. I am hoping that the progression of my thinking will be evident in my reflections as I progress through the book and learn more about how this can work in my classroom. Questions I ponder may well be answered in further chapters…

Introduction: Understanding the Urgency

What is it about Emily Moskam’s Math class that engages the students?

The students are all actively involved.

They can share or offer their ideas and build on each other’s ideas.

They get time to work by themselves and time to work with others.

The problems were interesting and challenging.

They can choose methods using whatever knowledge they possess and these can be informal or formal based on their ability, Therefore it doesn’t matter what level students are.

They are not told how to solve it so they own the process.

She’s obviously established a culture where it is ok to try things and fail and try again.

The learning is centred around the students and not her as the teacher. She is not demonstrating something to them and then they learn it. She is giving them a problem to encourage them to think about how to solve it themselves.

The problem is a real world problem with real world mathematics, therefore it is more authentic.

It isn’t black and white. There is no right way. Any method is valid but students can learn from each other if someone has a better method than theirs and they therefore may choose to adopt it.

What lesson can we learn and apply to our context/ year levels?

I learned so much here. Dinah Harvey has been preaching this stuff for years and I see more than ever that she was right. I feel very excited after only reading the introduction so far and am already visualising how I can make this work in my classroom.

I think the last few years my focus has been on meeting the national standards. I have been very successful in getting students to make accelerated progress in maths with regards to these standards but I haven’t done an especially great job at preparing them for ‘real world maths’. I have definitely been moving towards this more and more, particularly last year where I started to try to make my Maths programme more relevant and engaging. My focus has been on personalised learning which essentially involves students looking for their learning goals in their assessment data and deciding how to meet these.

Overall the majority of my students come away loving Maths because I am passionate and excited about Maths. I love it myself. I am also very positive and encouraging. There is a big ‘but’ coming here. I don’t think that I have prepared my students for the world with my teaching of maths. I have prepared them for high school by ensuring they meet the standards. Some how I need to find a balance between meeting a standard; personalised learning based on assessment data; real world maths; problem solving and evidenced achievement and assessment information, that proves progress is being made.

At my level, I can really see a place for this type of learning. My kids will love it. I know this. My concern is about how to achieve the balance I mentioned above.

What messages are our students receiving about Math?

Maths at school and maths in the real world are different.

Maths is about learning rules and formulae that you will never use again after school.

Being good at Maths means meeting standards.

I am good at Maths if I do well in Maths tests.

What would real Math look like? Can it be collaborative?

Problems that we actually face in the real world brought into the classroom. I think it would probably involve manipulating real life objects or even roleplay. In real life if you don’t know the ‘rule’ or method to solve a real mathematical problem, you need to use your brain to figure out how to work it out which may involve physically carrying out a task in a hands on kind of way rather than a formal written method kind of way. Learning to use the tools or resources within your surroundings is a great real life skill and I can see so much value in that for the workforce.

What negatives can you see or questions do you have after reading this chapter?

Not a negative but my role is to prepare students for high school (actually my real role is to prepare them for THE WORLD). Some how I need to make sure that if I am teaching content through problem solving that the students still learn all of the content within each strand. Therefore, my Maths problems will need to cover all aspects and I probably need a way to track that. Also I will need resources in the form of suitable rich questions that will actually cover all of that content. My thinking right now is that I would still teach strand units e.g. Geometry, Measurement, Statistics etc but I will need rich questions within those that cover everything high school students will need to know.

My brain is arguing with itself right now because I feel I’m contradicting myself. If students can really solve problems in any way they choose (with the right skills and a decent amount of maths knowledge), then they should be well prepared for high school if I teach through problem solving. The goal is to learn SKILLS NOT CONTENT KNOWLEDGE.

My concern is that high school maths is very much based on standardised testing, written algorithms, formulae and rules and NOT real world maths. It is very much based on knowledge and NOT skills.

Questions

1)     What shall I measure with regards to progress? Skills? Knowledge of content? Repertoire of strategies?  Achievement within curriculum levels according to mathematical progressions? All of the above? What is the priority and why?

2)     How can I measure it?

3)     How can I approach this problem solving style of teaching whilst still personalising learning for each student towards their learning goals? Where do these goals now come from? What will the students base them on? Will they be related to problem solving skills or the coverage of mathematical content?

Introduction: The Mathematics of Work and Life.

What is the place of Maths in the future? What skills, knowledge and dispositions will our students need?

Quote from the book:

‘Focus on performing computational manipulations is unlikely to prepare students for the problem solving demands of the high tech work place’.

Skills needed for the future include;

Flexibility, continuous learning, team work, collaboration, communication skills, persistence, problem solving, ability to think through problems and deal with situations when things go wrong, These skills are all transferable to areas aside from Maths.

How do we grow confidence in our students and a love of Maths?

Give them relevant, authentic, real world math problems so they can see a purpose for the learning after they leave school.

Teach them about the growth mindset and the fact that they can grow their ability in math as you aren’t born to be good at maths or not good at maths.

Make it fun.

Make it hands-on and practical.
Value all contributions.

Encourage learning from each other.

Encourage creativity, different perspectives, ideas and solutions.

Make it student centred and not teacher directed.

Teach them how to cope with and learn from failure.

Establish a positive learning culture in the classroom.

What does real life Maths look like? What generalizations and approximation do regular mathematicians apply to be successful?

Example from the book included the nurses measuring dosage.

Here some ways I use it in my life….

Measuring whilst baking.

Working out discounts in a shop.

Playing pool and working out where to hit a ball to make it go into a hole.

Counting calories and converting kilojoules into calories using estimation.

Working out how much paint is needed to paint the ceiling.

Calculating distance, speed etc when running, swimming. E.g. If it takes me 30seconds to swim 50metres, how long should it take me to swim 1km? What is my speed in km per hour?

Mixing cleaning solution with water using ratios

Volume of a container- how much liquid can it hold?

Budgeting

How much will the interest on my loan cost at X% over Y months?

Here are some things I apply to be successful….

I use a lot of rounding and estimation in my real life for maths. I use a ton of mental strategies to work things out and very rarely will use paper or a calculator.

I definitely rely on my times tables a lot and basic addition and subtraction so I feel that this is crucial to my use of more advanced strategies. I also regularly convert between fractions, decimals and percentages. I can easily convert between units of measurement to work out problems if necessary when measuring things.