July 6, 2015

Are you a math person? Is there such a thing, and, if so, does being a “math person” make all the difference when it comes to success in math?

According to Kimball and Smith (2013), there is one key difference between students who achieve in mathematics and those who don’t—entity orientation. Entity orientation is the belief that math ability is innate, the belief that you are either born with the circuitry to be a math person, or you—through the bad luck of the genetic draw—are born without that circuitry, destined not to be a “math person.” To borrow from Shakespeare, “2b ∨ ¬ 2b” (to be or not to be) is the essence of entity orientation.

Perhaps there is another way to think about mathematics and how orientation impacts achievement. With apologies to Robert Ludlum, let’s consider ways student achievement is less about genetic gifts and more about a “Bourne Identity.” Jason Bourne activated remarkable survival skills that had been honed over years of intense training to discover his true identity. Similarly, emerging mathematicians, led by effective teachers, develop their own remarkable mathematics skills bit by bit and over time. As a result, students understand that math achievement is earned rather than inherited.

This is an incremental orientation (Linehan, 1998), and, much like the growth mindset (Dweck, 2006), it is the belief that ability is not solely fixed at birth but instead attainable over time through guidance and work.

## The research on innate math ability

So, which is it? Is math ability innate or learned? Twin studies are often illuminating when it comes to questions of nature vs. nurture. In this case, unquestionably, a study of identical twins does show a degree of genetic propensity toward mathematics (Kovas, et al., 2007). This study suggests that genes account for 32–45 percent of mathematical skill among 10-year-olds.

Even so, Kimball argues (2014), 55–68 percent of achievement in mathematics is explained by things other than genetics. Among those “other things” are teacher expertise and the student’s commitment to learning.

The power of expertise and commitment becomes evident as the focus shifts from looking at inborn capacity for achievement to looking at the ability to grow. In a separate study of mathematics achievement, researchers found that **IQ does not predict growth in mathematics; it only determines a student’s starting point ** (Murayama, et al., 2012). Effective mathematics teachers and their students know a starting point to be just that—a place to begin. Starting points are finite. Growth is infinite.

## Acting like a math person

If the explanation of variance in mathematical achievement is found somewhat more in mindset than in circuitry, it seems appropriate that educators share ways to nurture an incremental—or growth—orientation. Kimball (2014) begins with the “love it and learn it” hypothesis, which is based in the concept that people who enjoy mathematics excel in mathematics. The challenge here is for teachers to develop in each student the appreciation for math or the ability to act like someone who likes math, and in doing so, lead each one to become better at math. People who love math:

- Speak the language of math
- Spend time thinking about and working on math

## The language of math starts with “facts”

The language of mathematics describes relationships among its key elements, including number, shape, sign, cosine, distance, and proportion. All of these together can get pretty heady and advanced, but the most fundamental of these elements is simply concerned with relationships between numbers. These relationships are expressed as a series of math facts.

According to Caron (2007), without mastery of math facts students are “virtually denied anything but minimal growth in any serious use of mathematics.” As a result, students who lack fluency may be challenged to develop the incremental orientation—the growth mindset—required for achievement.

As with any language, the pathway to mastery is most clear of obstacles in the early years. Yet, as vital as it is to develop math fact fluency during these years, by seventh grade only 42 percent of students own their multiplication facts, and less than a third own their division facts. And, because little attention is paid to fact fluency beyond the intermediate grades, it is a reasonable concern that these students may never gain the fluency and automaticity required for mathematics achievement (Baroody, 1985; Isaacs & Carroll, 1999).

## Thinking—and talking—about math

What is the benefit of getting students talking about math? Hess (2014) notes this brings to light their thinking about and working with math. For example, a student may give a correct answer despite having an incomplete understanding. Conversely, a student may know more than a problem requires but still arrive at the wrong answer. Students may own “working on math” yet still have room to grow in mathematical thinking and reasoning.

Extending the concepts of thinking, talking, and working like a mathematician, Hess recommends that teachers implement daily “DOK 3 discourse” by asking questions about math problems differently. Challenge students to find out if the problem can be solved in another way, and require them to provide evidence that the other way is based on solid reasoning. In essence, our students must do more than work like mathematicians. They must talk and think like them too.

## Escaping the trap of “2b ∨ ¬ 2b”

The solution to mathematical achievement is far more complex than can be determined through a single post, webinar, or study. That said, our growing understanding of unifying themes among these resources brings that solution within reach. It begins with acknowledging that **some mathematical ability is fixed, yet learning is not.** As documented, genetics explains approximately one-third to one-half of the variance in mathematical achievement. If my math is correct, that leaves slightly more than one-half to two-thirds of this variance open to the potential for:

- Incremental growth
- Mastering math fact fluency and automaticity
- Daily DOK 3 discourse—thinking, talking, and working like a mathematician—and acting like someone who likes math

## References

Baroody, A. J. (1985). Mastery of basic number combinations: Internalization of relationships or facts? *Journal of Research in Mathematics Education*, 16(2), 83–98.

Caron, T. (2007). Learning multiplication: The easy way. *Clearing House: A Journal of Educational Strategies, Issues, and Ideas*, 80(6), 278–282.

Dweck, C. (2006). Mindset: The new psychology of success. New York: Random House.

Hess, K. (2014, October 24). It’s time: How to “go deep” to meet the new math standards. Presentation at Educational Research in Action event, Renaissance Learning.

Isaacs, A. C., & Carroll, W. M. (1999). Strategies for basic-facts instruction. *Teaching Children Mathematics*, 5(9), 508–515.

Kimball, M. & Smith, N. (2013). The power of myth: There’s one key difference between kids who excel at math and those who don’t. Quartz. Retrieved from http://qz.com/139453/theres-one-key-difference-between-kids-who-excel-at-math-and-those-who-dont

Kimball, M. (2014). How to turn every child into a “math person.” Quartz. Retrieved from http://qz.com/245054/how-to-turn-every-child-into-a-math-person

Kovas, Y., Haworth, C. Petrill, S. & Plomin, R. (2007). The mathematical ability of 10-year-old boys and girls: Genetic and environmental etiology of t typical and low performance. *Journal of Learning Disabilities*, 40(6), 554–567.

Linehan, P, (1998). Conceptions of ability: Nature and impact across content areas. Purdue University ePubs. Available at http://docs.lib.purdue.edu/dissertations/AAI9921102

Ludlum, R. (1980). The Bourne Identity. New York: Random House.

Murayama, K., Pekrun, R., Lichtenfeld, S., & Rudolf vom Hofe, R., (2012). Predicting long-term growth in students’ mathematics achievement: The unique contributions of motivation and cognitive strategies. *Child Development*, 84(4), 1475–1490.

## Learn more

Discover solutions from Renaissance to boost math motivation and achievement in your school or district this year.