Math Mindsets

 

 

Originally Shared on:

http://ontariomathresources.blogspot.ca/2016/10/the-importance-of-growth-mindset-and.html

Big Ideas in Education

Big Ideas in Education

Growth Mindsets in Math are important for student learning. 

Our youngest students are often very excited about learning math. But then something happens. I believe that  a students diminishing excitement for math is directly related to a lack of a growth mindset.

What is a Growth Mindset? 

A Growth Mindset is a philosophy promoted by Dr. Carol Dweck. With a growth mindset, we each have the ability to achieve success beyond our innate abilities. We also have the option to move forward in the face of adversity, and become successful in our own right.

When it comes to math, there is no such thing as a ‘math person’. This is because a person’s true potential is always unknown, or unknowable.

But often, in school, we become focussed on getting the ‘correct’ answers, as fast as we can. This leads to students having fixed mindsets about their abilities in math.

In math, we want students to NOT feel shame that there are deficiencies – this is why we learn! We all have the capacity to learn through our efforts – AND through deliberate practice.

We also want students to understand that it is the process of learning that is important – not just the final product.

No matter where you are in your learning, you can always develop yourself further.

 Parents can go a long way to promote Growth Mindsets at home, Here’s How:

  • Avoid assuming that you are, or are not, a ‘math’ person. This can promote a fixed mindset in your child.
  • Have fun with math: Play math games, puzzles, cook and bake together!
  • Avoid praising speed when it comes to math
  • When a child gets an answer incorrect, instead focus on the process (logic), not the final answer (product) – try to find out what went wrong!
  • Praise your child’s ‘thinking’  rather than telling them how ‘smart’ they are. This helps students to understand that challenge is okay. Thinking that they are ‘smart’ can put pressure on them to think that struggling with math is a bad thing.
Deborah McCallum
Other Reference:

Positive Math Mindsets Flyer

growth_mindsets_and_math

https://www.smore.com/mf60t-growth-mindsets-and-math?embed=1

Math: How we Teach in the Classroom Matters

Our personal schemas about math greatly impacts how we feel about math and ultimately how we will perform in math.

From the time we are born, we are impacted by the attitudes and beliefs of those around us. The effects of nurture that shape our schemas of how the world works, also shapes what we believe, how we feel, and how we perform in math.

Can you imagine the far reaching effects of math anxiety on our economy? How does society cope with copious amounts of people avoiding jobs that include math? How can we change this? First, we will look at what math is, what causes math anxiety, and where we can focus our efforts into the future.

What is math?

Math is actually a whole schema of thinking. A schema that goes much deeper than the numbers that are assigned to things in our world.

According to Geist (2011), there is a serious dichotomy between a child’s own mathematical thinking compared to that which a teacher imposes in the classroom.  How a teacher approaches mathematics instruction also impacts math anxiety in children.

What does happen in the classroom that is so different from natural mathematical thinking processes?

The following are just some of the ways that anxiety becomes built into math:

  • We associating math with boring work.
  • The work students do in class is not related to daily life.
  • We believe that if we enjoy math, then we are not learning math
  • We rely heavily on cultivating memory through rote tasks
  • Mad minute and other bell work activities reinforce the idea that math needs to be done quickly and correctly
  • We treat students as if they have the same ability in math
  • We assume that there are not preferred ways of learning math, and pace of working
  • We believe that girls achieve due to hard work and boys achieve due to talent

http://www.gettyimages.com/detail/88621772

The approaches listed above then creates an environment and a mindset that math is a high risk activity. Math therefore becomes a source of deep anxiety for many students.

The research points toward girls being particularly affected by these practices and mindsets. Further, the research also shows that environmental variables change the results of math scores of children from lower income families.

We need new strategies. We need to be sensitive to the different needs of girls and boys. The fact is that every child learns differently and responds to different types of instructional approaches.

What we can do:

  • Move away from focusing on being correct, and move toward understanding the overarching concept
  • Promote understanding of math concepts over speed
  • Foster a learning environment that allows for critical thinking processes over rote memorization
  • Implement developmentally appropriate approaches for our students vs timed bell work
  • Seek out the strategies that we know do not increase math anxiety.

 

What strategies do you use that promote critical thinking and conceptual thinking of math in developmentally appropriate ways?

References:

Geist, E. (2011). The Anti-Anxiety Curriculum: Combating Math Anxiety in the Classroom. Journal of Instructional Psychology, Vol. 37, No. 1

http://joboaler.com/timed-tests-and-the-development-of-math-anxiety/

Math and Communication

The strategies we use to teach math are coming under a lot of consideration these days.

I do believe that curriculum frameworks are changing for the better within a changing society. We are moving from a purely behaviouralistic view of curriculum as drill, repetition, basic skills instruction and review. Curriculum under this view is highly prescriptive by nature, and requires step-by-step structured learning methods. However, I think that it is problematic to spend our time here for many reasons – one particular reason is because the answer to anything can be googled. 

It is important to focus on the language of math and our subjective realities that come into play when we are working with mathematical language.

Communication is therefore the cornerstone of math. Math makes use of symbols that we have given meaning to. Therefore, adding dimensions and new realities with communication is essential to creating a full understanding of the symbols and what they mean to others – and what they mean to us.

Constructivist views are concerned with thinking about how students learn – I agree that it is important to actively involve the student in the process of thinking and learning about math.

I also appreciate that we are moving toward phenomenological perspectives with our curriculum and finally starting to view individuals in relation to the work they are doing. It is important to get at the desires, feelings and understandings of our students – this is at the heart of self-esteem and is essential to learning.

Students must feel confident, eager to learn and have their work be satisfying. Don’t we all need this??

I think that math and problem solving also needs to account for, and incorporate individual creativity and student inquiry to these ends. Communication is essential for this to happen.

You may have different theories about math curriculum however, and we all need to come to our own theories.

Math Mindsets and Communication

photo 2 - Copy (9)

At this day in age, I am always surprised at how many mindsets about math still involve beliefs about drill worksheets and working out of a textbook. We are recognizing that how we communicate about math affects our mindsets. Positive math mindsets can boost student achievement in math.

Communication is just as important in math as it is in other subject areas. It is simply never enough to do basic drill and kill practice of multiplication facts. My philosophy is that the math facts need to be embedded within tasks and contexts that require creativity, problem solving and communication. I like to embed this within a ‘Gradual release of responsibility’ framework.

Gradual Release of Responsibility

The way I work with math literacy is actually very similar to how I work with language literacy in my classroom, and I keep in mind the gradual release model of responsibility for all students. I always start my lessons with the whole group. This is the opportunity to introduce the task, goals, vocabulary in addition to engaging in diagnostic assessment. This helps me to further determine how I will further adapt my instruction to meet the diverse needs of my students.

Talking circles is just one strategy that I use in my whole group instruction to create shared understandings and determine how students are thinking about the math. I am able to promote growth mindsets and a safe environment to have my students share and justify their strategies and ideas about our past learning, in addition to asking further questions and clarifying the answers of others, and set new goals. This is our opportunity to learn from each other in addition to honing in our own mathematical understanding.

We then may move toward a shared activity, this could either be as a whole class, but with me, more often than not, the students work in groups on key mathematical problems that build their knowledge and skills together. I am facilitating the learning by allowing students to get ‘stuck’, ask each other questions, try out multiple strategies based on what we have already talked about or done as a whole class. I am also there to help scribe, provide cues, more visuals, and any other strategies as in IEPs or as needed.

Sometimes, I work with guided groups. Here, I ask students to summarize for me, focus their attention on the key terms, concepts and strategies. I can be explicit again with what exactly they are learning and why, provide more examples and present material in sequenced steps if needed. I can also check for understanding and ensure that the students are understanding tasks and directions.

It is after this work, that I like to have groups present their strategies, using accountable talk, key knowledge and understanding. Sometimes we post up our work around the room after our presentations.

After this, the students engage in a gallery walk around the room with post-it notes – their task is to provide at least 2 questions to other groups about their strategies (lessons in asking strong questions occur in our class too:). After this, the groups go back up to their work and answer the questions for the class.

pattern_exemplars

It is now, that students have had lots of modelling, and a gradual release of responsibility with the concepts, that they can now move to their own individual work to demonstrate how they, or if they have been able to consolidate their learning. Those who are still not ready, sit at the back of the room with me in guided math groups, with further accommodations and modifications to ensure success.

I believe that effective communication is the backbone of math success. These are just strategies that naturally work for me.

What communication strategies work for you?

Resources:

Ministry of Education: Capacity Building Series:

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_Communication_Mathematics.pdf

Youcubed by Jo Boaler:

http://youcubed.stanford.edu/

Edugains

http://www.edugains.ca/resourcesLNS/MathResources/MathematicsResourceInventory.pdf

eWorkshop

http://www.eworkshop.on.ca/edu/pdf/Mod42_algebra_act_gr4.pdf

Deborah McCallum

copyright, 2015