Tag Archives: How to Learn Math

Enhancing Growth Mindset in Math – Learning together

We asked:

How might we, as a community of learners, grow in our knowledge and understanding to enhance the growth mindset of each of our young learners?

As a team, we have completed Jo Boaler’s How to Learn Math: For Students and have shared our thinking, understanding, and learning.

Blending online and face-to-face learning, we worked through the Stanford units outside of school so that we could explore and learn more when together.

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Here are some of the reflections shared by our team.

As a teacher my goal is to help children approach math and all subject areas with a growth mindset. It is of utmost importance that my students truly know that I believe in them and their ability to succeed!

Everyone my age should know that you should never equate being good at math with speed. Just because someone is a slower problem solver does not mean that they are a weak math student. Rather, sometimes the slower math thinkers are the strongest math thinkers because they are thinking about the problem on a deeper level. Being good at math is about being able to think deeply about the problem and making connections with it.

When talking to yourself about your work and learning new things, reminding yourself that you can try harder and improve is critical to potential success.  People are more willing to persevere through difficult tasks (and moments in life) when they engage in positive self talk.  

Mistakes and struggling, in life and in math, are the keys to learning, brain growth, and success.

Thinking slowly and deeply about math and new ideas is good and advantageous to your learning and growth.

Taking the time to think deeply about math problems is much more important than solving problems quickly.  The best mathematicians are the ones who embrace challenges and maintain a determined attitude when they do not arrive at quick and easy solutions.  

Number flexibility is so powerful for [students]. I love discussing how different students can arrive at the same answer but with multiple strategies. 

Working with others, hearing different strategies, and working strategically through problems with a group helps to look at problems in many different ways.

“I am giving you this feedback because I believe in you.”  As teachers, we always try to convey implicitly that we believe in our students, and that they are valued and loved in our class.  However, that explicit message is extraordinary.  It changes the entire perception of corrections or modifications to an essay–from “This is wrong, you need to make it right” to “I want to help you make this the best it can be,” a message we always intended to convey, but may not have been perceived.  

Good math thinkers think deeply and ask questions rather than speeding through for an answer.

Math is a topic that is filled with connections between big ideas.  Numbers are meant to be manipulated, and answers can be obtained through numerous pathways.  People who practice reasoning, discuss ideas with others, have a growth-mindset, and use positive mathematical strategies (as opposed to memorization) are the most successful.

We learn and share.

#ILoveMySchool

Visual: Encouraging mathematical flexibility #LL2LU

From Jo Boaler’s How to Learn Math: for Students:

People see mathematics in very different ways. And they can be very creative in solving problems. It is important to keep math creativity alive.

and

When you learn math in school, if a teacher shows you a method, think to yourself, what are the other ways of solving this? There are always others. Discuss them with your teacher or friends or parents. This will help you learn deeply.

I keep thinking about mathematical flexibility.  If serious about flexibility, how do we communicate to learners actions that they can take to practice?

Screen Shot 2014-08-19 at 8.05.42 PMScreen Shot 2014-08-19 at 7.58.42 PM

How might we narrow what separates high achievers from low achievers? If number flexibility is a gateway to success, what actions are we willing to take to encourage, build confidence, and illuminate multiple pathways to success?

 

 

Enhancing Growth Mindset in Math – Learning together

How might we, as a community of learners, grow in our knowledge and understanding to enhance the growth mindset of each of our young learners?  What if we enroll and take Jo Boaler’s How to Learn Math: For Students and share our thinking, understanding, and learning? What if we investigate and analyze the Common Core State Standards for the mathematics that we teach?

As a team of interested math learners, we will spend 10 hours (1 PLU of credit) learning together using the following outline as our course of study.

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In order to share our reflections, we will use a copy of the Enhancing Growth Mindset in Math Google doc to record, expand on, and share the reflections from the Stanford MOOC and our thoughts and connections to the CCSS.

It is my hope that each teacher-learner will share their reflections with everyone in the group or at least one other member.

How vulnerable will we be? What if we share what we know and don’t know and learn together?

 

Encouraging and anticipating mathematical flexibility

From Jo Boaler’s How to Learn Math: for Students:

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.

I wonder how many times I’ve taught “the one way” to solve a problem without considering other pathways for success. Yikes!

IMG_4846After completing Lesson 4 from How to Learn Math: for Students, A-Sunshine, my 4th grader, asked me to solve another multiplication problem.  I wondered how many ways I could show my work and demonstrate flexibility in numeracy.  The urge to solve this multiplication problem in the traditional way was strong, but how many ways could I show how to multiply 44 x 18? How flexible am I when it comes to numeracy? Is the traditional method the most efficient? Are there other ways to show 44 x 18 that might demonstrate understanding?

Screen Shot 2014-08-16 at 7.42.16 PMHow might offer opportunities to express flexibility? Will learners share thinking and strategies? How will we facilitate discussions where multiple ways to “be right” are discussed?  What if we embrace Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussion to anticipate, monitor, select, sequence, and make connections between student responses?

If my solutions represent the work and thinking of five different students, in what order would we sequence student sharing, and are we prepared to help make connections between different student responses?

How is flexibility encouraged and practiced? Is it expected? Is it anticipated?

And…does it stop with numbers? I don’t think so.  We want our learners of algebra to be flexible with

  • the slope-intercept, point-slope, and standard forms of a line and
  • the standard form, vertex form, and factored form of a parabola.

The list could go on and on.

How might we narrow what separates high achievers from low achievers? If number flexibility is a gateway to success, what actions are we willing to take to encourage, build confidence, and illuminate multiple pathways to success?

Have you signed up for EDUC115N: How to Learn Math? (it’s free)

Have you signed up for Jo Boaler’s online course, How to Learn Math, a free 8-session online course from Stanford University beginning on July 15? Do you hope to help learners enjoy and learn math? Do you wish you had more tools in your toolkit to help others continue to develop a growth mindset?

The course runs from July 15 through September 27, and learners work at their own pace through the eight concepts. From the overview:

Concepts:

  1. Knocking down the myths about math.
    Math is not about speed, memorization or learning lots of rules. There is no such thing as “math people” and non-math people. Girls are equally capable of the highest achievement. This session will include interviews with students.
  2. Math and Mindset.
    Participants will be encouraged to develop a growth mindset, they will see new evidence of the brain and learning and of how a growth mindset can change students’ learning trajectories and beliefs about math.
  3. Teaching Math for a Growth Mindset.
    This session will give strategies to teachers and parents for helping students develop a growth mindset and will include an interview with Carol Dweck.
  4. Mistakes, challenges & persistence.
    What is math persistence? Why are mistakes so important? How is math linked to creativity? This session will focus on the importance of mistakes, struggles and persistence.
  5. Conceptual Learning. Part I. Number sense
    Math is a conceptual subject- we will see evidence of the importance of conceptual thinking and participants will be given number problems that can be solved in many ways and represented visually.
  6. Conceptual Learning. Part 2. Connections, Representations, Questions.
    In this session we will look at and solve math problems at many different grade levels and see the difference in approaching them procedurally and conceptually. Interviews with successful users of math in different, interesting jobs (Sophie, film maker, Sebastian Thrun, inventor of self-driving cars etc) will show the importance of conceptual math.
  7. Appreciating Algebra.
    Participants will be asked to engage in problems illustrating the beautiful simplicity of a subject with which they may have had terrible experiences.
  8. Going From This Course to a New Mathematical Future.
    This session will review where you are, what you can do and the strategies you can use to be really successful.

Will you let me know if you register?