Preassessment, Part I

This is the longest I've gone without blogging in a while, maybe since I've started.  Feels very weird.  Definitely like I've been shirking.

Classes have started this week at Grand Valley, and I wanted to share from my two preassessments.  This first part is from giving the growth mindset survey to our preservice student teacher assistants.  The field experience for the professional program here is one semester in schools in the morning, where the TA teaches at least one unit for one class (though most do much more), and then a semester of traditional student teaching.  After our getting to know you time (Piece of Me plus student interviews of each other), I showed a Prezi on what do we mean by professional development (emphasis on student TEACHER rather than STUDENT teacher).

From the always funny Speed Bump.

Teacher, Teach Thyself on Prezi

Then we did the growth mindset survey.  (Developed with Sue Van Hattum.)  We discussed a few of the questions and made a human bargraph so we could see where people are.  A lot of agreement this semester, and a pretty reform minded bunch, I'd say.

 

So they're pretty countercultural about their beliefs about mathematics, and at least open to a growth mindset on the surface.  (There's lots of good research contrasting surface beliefs with the beliefs that cause actions.)  And they seem to be open to differentiation practices with how students learn math, strongly endorsing visuals, communication and questioning.  The question for Rebecca and I becomes how do we support and encourage them in this direction.  They are mostly placed in pairs (except for the odd man out), which we think will help, and did in the pilot pair placements.  I'm wondering if the hedging (mostly vs. strongly) is a sign of underlying belief vs. what we've been telling them in the university, or their developing belief vs. cultural truism.

Their comments about 10/15 and 18 were also interesting.

Pick one statement you agree with and explain.

8.  You can greatly change your ability to do math.

• The biggest thing you can change about math ability is your mindset.  If you believe you can’t, then you won’t be able.  If you believe you can do it, then you will be able to do it.  Might take some extra work.
• All things take help, and some take extra practice.

17.  Drawing pictures helps me to learn and do math.

• Being able to see the situation helps me organize. 
• Drawing pictures help me learn and do math.  They help me to see what is known and what  needs to be solved.

18. Explaining the idea to someone else helps me to learn math.

• Explaining forces one to view math in different ways.
• I have experienced this several times myself.  I want my students to have the chance to teach each other.
• It wasn’t till I started tutoring calculus that I started understanding the underlying complexities and the power of it all.
• You can say your answer and get it correct, but it doesn’t mean you know math.  You might know 2x3=6 from memorization, but if you can’t say why then you do not know math.
• Explaining helps me check and see it in a different way.
• After trying a problem it helps to clarify a question or reinforces my confidence.
• Forces you to put your thoughts in a logical order and may force you to see the problem in a new light – how the other person sees it.  
• Helps you learn because it is a good measurement of how well you know something.  It’s easy to explain to yourself, but explaining it to someone else helps a lot.
• To explain it is to know it so well that you can approach the idea from any angle.

Pick one statement you disagree with and explain.
2.  How intelligent you are mostly determines how well you can do math.

• There are many subjects and you can be intelligent without math.

3. How well you can memorize mostly determines how well you can do math.

• Memorization gets a correct answer not understanding.

5.  Boys/men are better at math than girls/women.

• Girls can do anything as well as boys. (Look around the room.)

9.  How fast you can get a correct answer is a good measure of math ability.

• You might be the slowest person at getting an answer, but make less mistakes or just need time.

10.  The percent of correct answers on a test is a good measure of math ability.

• Could be chance.
• There are so many factors that go into taking a test.

11.  The is one right way to do a math problem.

• Never is there one way.

15.  You need to focus on getting the right answer to do well in math.

• You can understand each step and make a simple mistake and get the wrong answer. 
• Students can learn a lot on the way of solving a probem.   
• Math is about learning the process.  That is the most important thing. 
• The right answer may be wrong from rounding error, etc…

Rate your mathematics ability from 0 (none) to 10 (could be a mathematician):

Let me state unequivocally: I have every confidence in each of these teachers' mathematical ability.  This is a measure of their self-perception, not their competence.

5
6 6
7 7 7 7
8 8.5
9 9 9
10

This makes me wonder about our schooling.  Why don't they all consider themselves mathematicians?  What damage have we done?  If a college math major with a 2.8 GPA minimum is a 5, what is a struggling high school student?

So, that's my data.  It has me very hopeful for the semester.  I'll be working to support them in their fledgling positive beliefs (hoping their data supports it, too), and in helping them transfer those solid math beliefs to teaching.

What do you see in this data?  I'd love to hear in the comments, if you have the inclination.

Growth Model

Dweck.

Last summer, my colleague Dave Coffey's summer reading revolved around the idea of a growth mindset and its relationahip with learning.  Carol Dweck is the most often cited researcher in this field.  There's a pretty good piece on her and the related research in a recent Chronicle of Higher Education article.  Some of her ideas have been popularized by Daniel Pink.  (Jamie Feild Baker has a post about that connection.)  There's a commercialization of her work by Brainology, that seems to be based on proving to students that this brain research is true by showing them it's how their brain works.  (Brainology is also on Twitter, it turns out. Not bad linkage.)

The oversimplified summary of the research is that people's growth is limited by their own assessment of their possibility for growth.  People who think ability is fixed find it hard to grow.  People who think it's possible to grow find it hard not to.

My response was to try asking Dr. Dweck's questions of my future teachers and see what happened.  It was definitely interesting, and the discussion of the growth mindset idea was definitely a great discussion.  But there's always so much to do, that I just let it slide.

Recently Sue Van Hattum (aka Math Mama Writes) posted that she was thinking about it also and put up a sample questionaire.  I dug up the one I had given last fall to send her, and then started thinking about making it more math-centered.  And that's what I wanted to share today.  I merged them with some mathematical process questions I had used before, and a few other math attitude chestnuts.  I am more and more convinced that assessment and evaluation is where I need to concentrate so that I can teach my actual students and not figments of my imagination.

Dweck's original questions (2 forms)

Implicit Theories of Intelligence Self-Eval.v2 by goldenoj

Modified for math

Implicit Theory of Mathematics Learning by goldenoj