by Vicki So, Rubicon International
Some numbers to think about:
- 37% of adults recall that they “hated” math in school (AP-AOL, 2005)
- 71% of adults could not calculate miles per gallon on a trip (Phillips, 2007)
- 58% of adults were unable to calculate a 10% for lunch bill (Phillips, 2007)
- 15% of adults said they wished that they had learned more or studied more math in school (Phillips, 2007)
Me + Math = Anxiety
As an Asian-American, I have hugely benefited from the stereotype of being “good at math.” One time, my Geometry teacher Mr. Erlich wrote me up for being repeatedly tardy to class. I can still see his cursive handwriting on the detention slip: “You can attend Math Team practice instead.”
My teachers never grasped that math often gave me anxiety– the heart-pounding-kind when my name was called to answer a question, or the frustrated-to-tears-kind when Mom or Dad tried to help with homework. I worked hard and memorized formulas, but that Asian mathmagic never came to me the way some expected. You can imagine the Math Team’s disappointment in me. But at least I got cool t-shirts that say things like, “The Denominator” or “Mmm… π”.
What if the adults in my life had paused to ask how I felt about math? Similar to reading inventories, could an attitudes survey help pinpoint math interventions for students? Would this process reveal inherent biases, misconceptions, or counterproductive beliefs about math, not only for students but for teachers, parents, and other stakeholders?
Example:
Figure 1 Mathematics Survey
- To be good at math, you need to… because…
- Math is hard when…
- Math is easy when…
- How can math help you?
- The best thing about math is…
- If you have trouble solving a problem in math, what do you do?
Tell anything else you want about math.
On the back of your paper, draw a picture that shows what math means to you.
These are the questions that Phyllis Whitin poses in The Mathematics Survey: A Tool for Assessing Attitudes and Dispositions. For secondary examples, try here or here
These are the student survey questions that Phyllis Whitin poses in The Mathematics Survey: A Tool for Assessing Attitudes and Dispositions. Specifically, Whitin investigates the ways to develop a classroom environment that builds more positive attitudes toward math by surveying fourth-grade children over a four-year period (2007). For example, the student who responded with “Math is hard when… you can’t understand what the teacher says” suggests a belief that mathematics is a solitary endeavor dependent on paying attention to the teacher. Whitin then challenges teachers to ask themselves tough questions including:
- What do these responses reveal about students’ perceptions regarding the teacher-student relationship? Regarding student-student relationships? Do references to the teacher imply that the teacher is the sole source of knowledge? Is there evidence of student autonomy? Of collaborative thinking? Are other students mentioned? If so, in what ways?
- What do these responses reveal about student perceptions regarding mathematical content and applications? Do students cite examples of functional applications of mathematical ideas? Do they view mathematics as valuable and relevant in both the present and future?
- What do these response reveal about students’ perceptions regarding processes of engaging in mathematical investigations? Do the students view the challenge as rewarding?
After reviewing the responses, Whitin identifies four major trends and associates each trend with a positive shift in attitude, dispositions, and beliefs. She also recommends changes to teacher instructional plans, including a “reflective conversation that specifically addressed the targeted disposition” at the end of each task or activity (2007).
Trends Implied by the Surveys
Positive Attitudes, Dispositions, Beliefs
Instructional Plans for Change
Unproductive Beliefs
Students possess different innate levels of ability in mathematics, and these cannot be changed by instruction. Certain groups or individuals have it while others do not.
Productive Beliefs
Mathematics ability is a function of opportunity, experience, and effort— not of innate intelligence. All students are capable of participating and achieving in mathematics, and all deserve support to achieve the highest levels.“She’s just not a math person.” We’ve all heard this before. Several studies by Carol Dweck and Angela Duckworthargue that these labels imply that intelligence is “fixed” and inadvertently limit the potential of children. In fact, a “growth mindset” and perseverance through obstacles is what leads to later success in life (see my other blogpost on “Establishing a Growth Mindset”).
The cognitive research compares learning math to learning to read— “we can do it, but it takes and effort, and requires mastering increasingly complex skills and content… even if not everyone wants to reach the point of comprehending James Joyce’s Ulysses or solving partial differential equations” (Willingham, 2009).
Howard Gardner also attempts to set the record straight that his theory multiple intelligences should not be equated with student learning style. “ should recognize that these labels may be unhelpful, at best, and ill-conceived at worst.”
Unproductive Beliefs
Students can learn to apply mathematics only after they have mastered the basic skills.
Productive Beliefs
Students can learn mathematics through exploring and solving contextual and mathematical problems.Understanding by Design’s Grant Wiggins offers his candid insight on conceptual understanding:
“The Common Core Standards in Mathematics stress the importance of conceptual understanding as a key component of mathematical expertise. Alas, in my experience, many math teachers do not understand conceptual understanding. Far too many think that if students know all the definitions and rules, then they possess such understanding. The Standards themselves arguably offer too little for confused educators.”
Don’t my students need a balance of both procedural and conceptual knowledge?
Unproductive Beliefs
An effective teacher makes the mathematics easy for students by guiding them step by step through problem solving to ensure that they are not frustrated or confused.
Productive Beliefs
An effective teacher provides students with appropriate challenge, encourages perseverance in solving problems, and supports productive struggle in learning mathematics.On the one hand, I know it is important for my students to feel initial success. On the other hand, I know that my students should value perseverance in order to succeed in the long-term. How do I find the elusive Goldilocks zone of “appropriate challenge” or “productive struggle”? Dan Meyer explains how in his blog and TED Talk “Math Class Needs a Makeover”
Margaret Schwan Smith and Mary Kay Stein also provide the research behind Selecting and Creating Mathematical Tasks, or classifying math tasks into lower-level and higher-level demands. The article includes a great activity to try at your next Math meeting.
Last but not least, several organizations like Milestones and Be a Learning Hero are devoted to helping Parents and Guardians understand the Common Core through grade-level specific videos, homework help, and more.
