EDUC115N How to Learn Math Final Post

This is my final review of the EDUC115N class: How to Learn Math.

I want to troll through the resources and link to the most valuable items that I am going to put to use in my math class.

Developing a Growth Mindset

All students can learn math, but they don't know that yet, and juggling, yes juggling, can help teach them that. We are going to start our math class learning how to juggle. I need students to understand that with the proper instruction and the proper mindset that they can learn anything. They should also begin to understand how it is the brain works.

Goal #1

• Students Develop a Growth Mindset
• Students Learn how the Brain Learns

After this we will use an activity called number talks each and every day. We do not leave the first two goals behind forever. We revisit those ideas over and over, but we also build on them. The class needs to practice making mistakes and celebrating them, using them to learn and eventually realize that mistakes are where the real learning happens.

Goal #2

• Students become comfortable making mistakes
• Students begin to develop number sense 

Number talks is basically where the teacher gives the class an equation to solve mentally. Students do the mental calculations. Students’ strategies are shared and discussed to help all students think more flexibly as they work with numbers and operations.

For example: 9.8 + 8.7

1. Get students to estimate before attempting to solve. 
2. Ask students to mentally solve the problem.
3. Have them explain to partners and the class how they solved the problem.

It's much more involved than this, but the idea is that students see different ways to solve things, they are free to make mistakes and they develop language and thinking skills needed for math.

Students should talk to each other and the teacher about ideas – Why did I choose this method? Does it work in other cases?  How is the method similar or different to methods other people used?   

Goal #3

• Students see themselves as capable at learning and succeeding in math
• Students think creatively and openly about numbers 

Mathematics classrooms should be places where students believe:

1. Everyone can do well in math
2. Mathematics Problems can be solved with many different insights and methods
3. Mistakes are valuable, they encourage brain growth and learning

EDUC115N Review #9

I am going to post one of my answers to a question in the course. This is about the process that students need to use when encountering math problems.

My metaphor: Brain Building Construction Zone

Students will be taught the metaphor that doing math is like building your brain, and every math problem is a brain building construction zone. 

When given a math problem you don't just jump in and start building the answer you have to slow down and read the signs. Students will be taught that in this construction project, when given math problems to solve there are important steps to follow: 1) Say it 2) Draw it 3) Estimate it. These are the pre-building steps that students need to slow down and pay attention to. If they don't understand enough to make an estimate than they need to stop and go back to the drawing board. This is like making an estimate for a customer. Before they build they need to be able to describe what their end product should look like, just like in the buildings and materials trades. 

Pre:Build = Before Solving
1) Say it 2) Draw it 3) Estimate it

Once their customer has agreed to their estimate then they can build. To build they need all their math tools, and they need the right tools for the job. Most of the explicit teacher directed math lessons will happen here. Sometimes they may not have the tools and may need to learn how to use new tools. 

Here is a math tool. 

When they have mathematized they need to test their building project and refine or revise as needed. Once done they step back and look at their project to see if it is ready to be sold. Can they describe it to a potential buyer in a way that makes sense. Has their project actually been built, or is it just a mess of math material that nobody understands?

Describe it and revise if needed.

To recap. In the math brain building construction zone, stop and read the signs, then say it, draw it, estimate it. Then build it with your math tools. Make sure it is perfect by refining and revising. Then sell it to the customer by describing it in a way that makes sense.

The process will help students see math as a creative act that they control. 

EDUC115N Review #8

Number Talks #2

In my last post I introduced the idea of number talks. As I worked through session five of the How to Learn Math course I was shown examples of number talks from a college classroom and a grade three classroom. Granted the students in the college classroom were being taught how to use number talks, but the task still helped them understand math on a different level. 

One of the thing I am noticing is that students need to have a firm grasp of the times tables for this level of math to work, so as I think about teaching my strategies class part of the class will have to be dedicated to helping students memorize the times tables. Number talks can help with this, but I really believe the times tables will have to be visited everyday.

One method used in the number talks lessons was the use of dot cards. Students were shown dot cards and asked to describe to their peers how they added up the number of dots. This process had students talking mathematically and with precision. The teacher then created visualizations of what they were saying. It was really quite surprising seeing how ten dots on a piece of paper helped students learn the key lessons: numbers can be broken down, they can be manipulated, they can be decomposed into "friendly numbers."

After the dot cards lesson I saw how number talks were used to develop an understanding that math is far from static or concrete. Number talks gets students talking about creative, but precise, ways to solve problems in their heads. It gets students doing the talking and the explaining instead of the teacher, and number talks concludes with a visual representation of what was solved. This is a practice that will work in a jr. high classroom. 

EDUC115N Review #7

Now we are getting into the meat of this course. The work of developing a growth mindset is a year-long pedagogical guiding point, one that needs to be taught, developed, revisited and reflected upon, but what should the day to day math lessons look like? I know some big ideas have been mentioned in the class, and here in this blog. Students need to make sense of numbers, talk with each other when trying to solve problems and be given the space to think creatively about math, but again, what about specific lessons.

Enter Number Talks. An idea and a method of teaching that can be used everyday in the math classroom, in order to increase fluency and automaticity, and, at the same time, help students with the conceptual understanding of numbers.

Not Quite what I meant

Number Talks is all about freeing a students mind from thinking that there is only one way, one right way to solve problems in math, and it works like this:

1. Give a problem with the instructions that you can't write it down or use the traditional method of solving it. ex) 18 times 5
2. Have students share and describe how they got to the correct answer. At this point students are learning a) how to talk about numbers or b) how other students think about numbers.
3. Talk about the different methods that are used. Here the teacher can step in and create visual representations of the student's explanations. Many of the rules of mathematics can be explicitly taught here.  

Having kids solve problems in different ways teaches them number sense. It teaches them the ability to break numbers apart, or decompose the numbers, and regroup them. This ability is a key foundation for all of math. It also teaches that math is creative and flexible. With activities like number talks students walk away from their math lessons understanding numbers, instead of blindly remembering and following formulas. 

EDUC115N Review #6

This is the half-way point of this course, and I want to offer a little review of the major idea of the course. I was able to tell a family member about this course yesterday, and he asked me, "so what does have to say about how to learn math?" I was happy that I actually had an answer to provide.

Stanford, through prof. Jo Boaler, is very clear about what students need in order to learn math. Students need to develop a growth mindset. They need to know and believe that they, everyone, can learn and understand math. Not as a, "you can do it!" false self-esteem thing, but as a fact about their brains, "anyone is capable, with hard-work practice and the right teaching methods, capable of succeeding at math. Students need to be taught how their brains work, given the opportunity to experience real learning, and reminded often that all students are capable of growing their understanding.

How we teach, allowing students to struggle, talk to one another, find different approaches, and make sense of the math they learning. How we help students in the classroom, praising mistakes, withholding answers, keeping things open to students thinking. How we assess, providing feedback instead of grades, celebrating mistakes as opportunities for learning, focusing on growth. All of those things, that is how students learn math.

EDUC115N Review #5

This is one of the posts I have been wanting to write because it concerns a topic I have often discussed with colleagues and people not in education. Many many teachers and even more people not professionally involved in education believe that ability based groupings of students makes sense, is best for students and is the most effective way of organizing a school in order to help teachers be successful. I have always disagreed with ability based groupings, and it turns out, so does professor Jo Boaler, professor of Mathematics Education at Stanford University.

One of the reasons people like ability grouping is because it makes sense in their normal life, and in their learning outside of school. Someone that has never done Yoga would not enter into an advanced yoga class, and why would someone that is great and experienced at Yoga go to a beginners class?

Not for beginners

The question is, should schools, particularly jr. high schools take the common sense approach called ability grouping or tracking?
The answer is no, and here is why: it encourages, in all students, a fixed mindset. Whether a student is placed in the high, medium or low group they develop fixed ideas about their ability. Even the students in the high group think they are there, not because they work hard and persevere when given challenging work, but because they are the smart kids. When students realize they are in the low group everything begins to unravel. The EDUC115N course says it nicely.

There are many pieces of research, and other valid reasons for why ability grouping just doesn't work. The Fixed mindset versus a growth mindset is one of the most compelling. 

EDUC115N Review #4

I am eager to share some thoughts that have come in this class about ability grouping, but I am going to save that for my next blog post. This one will be short and it will be about assessment.

In the How to Learn Math class that I taking one of the ideas discussed is the value of formative assessment. Now, teachers at my school are relatively progressive about assessment, so they are already quite aware of these ideas, but there are a couple of notions that deserve to be heard again and again.

but it's a valuable story

1.  Feedback is more valuable to a student's learning than a grade. "Students who only got feedback scored significantly higher than ones given a grade or a grade and feedback." The best thing you can do for your students is to ditch the grade and give them diagnostic feedback.
2. Students need the opportunity to practice self and peer assessment. What would this look like in the math classroom? Students given access to the learning goal of a given lesson and assess where they are in their understanding. Then students are given the opportunity to work with each other, problem solve together, discuss solutions and peer assess each others ability according to the lessons learning goal. 
3. After low achieving students spend time discussing and assessing themselves and others they will start behaving like high achieving students. 

This is what assessment in the math classroom needs to look like. It is tradition and the need to classify and group students that insist on having big unit exams with grades given to students. These are not necessary practices, and are in fact harmful because they create a fixed math mindset in students.

I know that this is controversial, but wait until the next blog post...

EDUC115N Reflection #3

Lots of great ideas in session four, but I think the best way to share what I am learning is to share what I am learning. Check out the link below to see the difference between how math is taught and how math ought to be taught.

When I let them own the Problem

Here are my ideas about the problem:
The initial wonder, creativity, and questioning would be so much more interesting to students than a problem in a textbook. I also appreciate how students would have to measure the lines and angles that they drew with ruler and protractor. All of the questions in a text book have nice rounded distances and angles for students to work with that they never get to apply their measurement and drafting skills to an actual problem. Bringing real life measurements into the math problem will develop skills that the students need. Students need to be open to different methods of solving a problem. There is not only one way to do it, but in order to reinforce the lesson, and in order to make sure students have achieved the learning goals, having students work on each others drawings is brilliant. As always, making students explain to each other puts even more learning on the students. I can hear the math teachers I work with objecting that the teacher who wrote this blog took a 20 minute lesson and turned it into a lesson that would take two classes, but the results are worth the time it would take. Instead of only 40% of the class understanding and only 10% of the class enjoying the lesson the teacher should have 100% of the class understanding, 40% of the class having a deep understanding and almost all of the class also enjoying the creativity, skill development, and real world application of math.

Which type of math question will create future engineers?

EDUC115N Reflection #2

Now that I can access google apps again, here is what I am taking away and will use from my Stanford online math course.

The math classroom matters. The environment that is created for the students when they enter and experience the math classroom is crucial. When I talk about the environment I really mean the mental environment. How one physically organizes and decorates the classroom can impact the mental environment, but it really comes down to how the students feel when they sit down and begin to learn math.

Students need to feel safe to make mistakes.The importance of speed needs to be eliminated. A growth mindset, as opposed to a fixed mindset, needs to be taught and encouraged. These three ideas will almost certainly run counter to a student's pre-existing ideas about the math classroom, so they will have to be explicitly taught and modelled. Mistakes will have to be celebrated, the teacher will need to prove to students that all are capable of learning math and growing as a person, and assessment practices will need to change. 

To stick with this assessment idea a moment longer. What does it mean to be successful in the math classroom. Traditionally it means getting through the curriculum and doing well on math tests. Is that really creating students that will have successful careers in Science, Technology, Engineering and Math? Of course not. Our assessment practices need to encourage a growth mindset by providing positive individual feedback. We need to stop moving through the curriculum before all students have experienced success with the content. 

Just to reiterate, the ideas above are coming from Stanford math professors. More to come...

How to Learn Math: EDUCN115 from Stanford University

I will use this space over the summer to share and reflect on my experience taking a free online course from Stanford University titled: How to Learn Math.

The fact that there I can take, for free, a course from an Ivy league school is exciting and potentially powerful. We will see.

The first thing about this class that I am excited about is that there will be a course for students offered in the Fall. I hope I can register our strategies students, if this turns out to be a good course for them.

Positive experience with the course #1: Click pause, change a diaper, back to math class.

Key take aways from the introductory session:

1. Make sure your students know that you have high standards, and that you believe in their ability to achieve them.
2. Math stereotypes can be debilitating and need to be actively combated. 
3. Students should use their imagination in the math classroom. Indeed, it could be the only subject that can operated unencumbered by reality. Why imagining a perfect circle should be an artistic endeavour.