Chapter 4-The Importance of Flexibility

For this blog post I've decided to select a few quotes from chapter 4 and to reflect on each of them.

".the joy and fascination young children experience with mathematics are quickly replaced by dread and dislike when they start school mathematics....."

-my second son shows a lot of interest in counting items or finding numbers on labels, or counting with his cousin so they can race or play hide and seek.   Other times you hear him invite everyone for "tea time" ensuring we all have matching cups and sauces.  He creates yellow and red patterns with his magnoformers (something that was never directly shown to him).  I can't help but wonder what will happen to his joy for learning and exploring when he is exposed to school mathematics. At what point will educators shift their thinking from I have to cover the curriculum to here is where my students are in their development what am I going to do to support them?

"When students see mathematics as a set of ideas and relationships and their role as one of thinking about the ideas, and making sense of them, they have a mathematical mindset."

-I wonder what would be the response from students if they were to be asked: what is you role as a math student?"
-I also wonder how different that response would be from students at other schools


".....number sense and mathematical mindsets develop together, and learning about ways to develop one helps the development of the other."
-As the numeracy teacher, I share in the responsibility (with classroom teacher and student) to help students develop flexibility with numbers as number sense is needed in all areas of mathematics but more importantly to see connections and relationships between ideas/concepts.


Any thoughts on these or other quotes from this chapter?

Youcubed!

Lots of great ideas in Mathematical Mindsets!  I've explored youcubed.org a bit. Very user friendly.  I like the background information; not too overwhelming.  I think it might  be my new favourite go to resource. 

Chapter 5: Rich Mathematical Tasks

As I was reading this chapter, I reflected on the math tasks I provide to my students and wondered if they met the criteria of a rich task as provided by Jo Boaler. Another question that came into my head is, what do students think a rich, engaging task is. Is it enough for teachers of math to know the criteria of a rich, engaging task? Shouldn't students opinions about a task matter? If we want a growth mindset in the math classroom, the criteria for an engaging task should come from the students. If students create criteria for what an engaging task in math is, then they can easily start any math task, they think is engaging, with a positive mind, ready for struggle, arguments, multiple perspectives and approaches.

This was our math lesson today:

We listed some math tasks we have already worked on that we found engaging. Yes, Ms. Powell, a lot of my students thought that the Chocolongo Bar problem was an engaging task!

Next we worked on the following engaging task from the book.

As students worked on the task, I asked them to think about two things: Is this task engaging? If yes, why? I walked around and started recording some math talk. 

 

 

 

Then, in groups students created criteria for what makes a math task engaging.

We started to look for similarities we looked for similarities and co-created criteria as a class

Now compare what students came up with, with Jo Boaler's criteria...there are marked similarities. 

it is imperative to know what students think is engaging. After all they are the ones who have to be engaged in the task and it is their engagement that would lead to a positive learning experience. This activity was also a good exercise in metacognition. Students had to think about their thinking.

Chapter 6: Are we gender-biased as teachers of math?

I wrote this post before I read chapter 6.  After reading this chapter, I saw an even deeper connection.
Gender equity and mindset have always held a deep fascination for me. I think it is the product of the environment I grew up in and went to school in  that forces me to think about my professional life as being something different if I had the same opportunities to learn and think as boys my age. Even though I had the opportunities at home,  the schooling system in India in the eighties did not provide me with the same.
As I was scanning through Twitter, I came across this post by a high school math teacher in Hawaii.
http://mobile.edweek.org/c.jsp?cid=25920011&item=http%3A%2F%2Fapi.edweek.org%2Fv1%2Fblog%2F182%2F%3Fuuid%3D57299&intc=bs&cmp=SOC-SHR-GEN
My immediate connection was to our blog but in a flipped way. Interestingly, we have a strong female presence in teaching and learning math in our school. But I do observe a lot of male math presence on Twitter. Is it a growth mindset that we unknowingly instil in male students that they can be good at math or is it the demands of math-centred professions on our male students that makes them think they are good at math? I have experienced in my own classroom how some male students say with confidence and belief that they are good at math. To date, I have never heard a female student say the same even though my female students are strong mathematical thinkers too.

Mathematical Mindsets Celebrate Process NOT Product

Chapters 3-4

Real math should celebrate the process that mathematical mindsets go through as they engage in rich, real-life, meaningful math tasks and not just the end result. When students continue to focus on the right 'answer' in math, they completely miss the thinking that happened before getting to the answer. Is this because, as teachers, we continue to focus on and reward the right answer and are at a loss about what to do with students whose answer is incorrect even though they used some thinking strategies to get to this incorrect answer? As I read this book, I want to apply what I am reading to real classroom contexts and record the change, growth or not, in the way my students are beginning to think about math. I would like to share some strategies I have been trying in class and their impact on student thinking and attitude. My hope is to build a repertoire of strategies from my own experiences and others' blogs or responses that can be used as concrete examples of how we create a growth mindset. It was interesting when Ms. Gelinas mentioned to me the question that was asked in the recent IB test. The question showed two bags of apples and asked, which one is more, 2/3 or 2/5? The interesting part was that students were told that the test did not care about the answer of this question but how students problem-solve. 

 These are the strategies I tried, to focus on process not product:
1. Students were asked to use the word 'solution' not answer for any math task they were doing. Just a little change in language changed the connotation and expectations associated with the task for many students. The word 'answer' has a connotation that there can be only one right answer but the word solution, for some reason focuses on the problem and the task more than the end result.
2. I assigned a test to the class and told them that they would only be marked on the thinking and communication and can receive an 'A' even if their solution is not correct. This really amazed some of the students. They actually asked me how this was possible. A lot of our students truly believe that if their answer is incorrect, all is lost. Unfortunately we have instilled this feeling in their minds. In this assessment, students were asked to spend all their time in communicating about their thinking and not worry about the solution. 

Hi All,
Some of us were wondering if we should create a structure or a loose framework in which to respond so every one gets a chance to reflect on their own as well as others' readings and posts. I know that some of us are involved in report cards and this is a busy time of the year. I know that I have read till chapter two and have blogged. If some of you have gone ahead, that is great, but would it be okay if we can restrain ourselves from blogging till about chapter two so everyone can catch up. We will continue to blog if we wish to or wait until report cards are over. Hope this is okay with everyone.

I can finally contribute!

After solving some technical difficulties (thanks Monica), I'm finally on.

I probably won't be contributing much though until after report cards.  Sorry :(.

Mistakes in Life: Celebrating Failures

While reading the chapter on mistakes and struggles, I couldn't help but think about young math learner Carlene, teachers' college, and Numeracy teacher Carlene.  As a young learner, I always struggled with math; a language that intrigued me. I don't recall worrying about failing anything because my parents were very supportive and always encouraged me to do my best, but I was worried about my peers knowing about my struggles with math especially K.W.  Everyone knew K.W. got perfect on every test/quiz.  I am that student who needs time to think and to discuss my ideas and hear other's ideas. We always worked independently. I use to look for the answers at the back of the textbook and then try to figure out how to arrive at the answer.   I admired K. W. and wanted to understand math just like him.  Fast forward to teachers' college where my path to becoming a math teacher began.  Dr. Andrew Allen is the math professor at university of Windsor who changed my perspective about mathematics.  I clearly recall him telling us that we should celebrate failures with our students just as we would their successes.  When I was hired to teach in PEEL, I struggled with teaching math, the way Dr. Allen talked about, through problem solving in a collaborative community of learners, mainly because I didn't have a partner with similar philosophy.  I had such a hard time with parents not understanding the approach; one even wanted their child removed from my class. I refused to conform. I did a lot of research on my own which I used as talking points with parents, have had supportive administrators and would eventually meet Shannon Lee.  As a Numeracy teacher I encourage students to own their mistakes and share their struggles.  It's not enough for students to say "I made a mistake" or "I can learn from my mistakes." I challenge them to dig deeper and explain what they mean.  How do you know that you have made a mistake? What did you learn from someone else's mistake or your own? How did you overcome your struggles?  It use to be hard to watch students struggle, but now I smile every time I see it or hear it cause I know they'll be stronger learners because of it!

Chapters? Blog as we see fit?

Are we reading and discussing the book as chapters or pages or would you like to just blog as you read and make connections? 

The Power of Mistakes and Struggle
Today, the math in my class was all about the struggle. I posed a challenging problem in class and I was hoping to look for strategies children were using as they struggled. I also noticed children's body language and facial expression as they struggled. It was interesting to see that most of them were trying something to figure out the 'answer', the 'right' answer. When they felt they had the answer, their math talk stopped. There was nothing more left for them to do as in their minds they were 'done'. It is interesting that the messages we send about mistakes and wrong answers as well as about right answers really lead to the way student act in class. In fact I struggled to debrief the math today because it was really students' attitude I was debriefing and not the math strategies themselves. Nancy, my teaching partner suggested that I should ask students what they did when they were struggling. I read parts of pages 2-4 from the book to the students and they were quite amazed with the idea of "brain plasticity" and the possibility of our brains to grow.