By Jan Bryan, EdD, Vice President, National Education Officer
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 inborne 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
Do you have ideas for turning each student into a math person? How do you get your students talking and acting like mathematicians? Please share in the comments below. In addition, check out our free eBook on what a great mathematician looks like!
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. [Video File]. Retrieved from https://www.youtube.com/watch?v=vfSNvjJHViA&feature=youtu.be
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). 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 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.
10 Comments
The ideas suggested in this article correspond well to my anecdotal observations working with math learners in the classroom. Math problem solvers and algebra learners who are not fluent in math facts expend great effort and energy on simple calculations, distracting them from the patient, critical thinking required for application and abstract concepts of math. Math learners become more capable when their math coaches believe they can.
Thank you for your comment Allison. I am particularly intrigued by your description of the “patient, critical thinking required for application and abstract concepts of math.” I had yet to see “patience” described as part of entity or incremental orientation, mindset or critical thinking, but the way you’ve developed the association among fact fluency, automaticity, and critical thinking is eye-opening. I look forward to learning more about this key attribute in learning. jb
Interestingly I just finished a paper for a graduate course I’m taking on the topic of math anxiety and personality traits. Certainly it was clear from the research that a tendency towards math anxiety is personality based. What I was not expecting to find was some evidence that at the earliest stages of math anxiety, with young students, there is not necessarily a math calculation skill gap (Krinzinger, H., Kaufmann, L., Willmes, K., 2009, Math anxiety and math ability in early primary school years). Very little work has been done with students just prior and during the development of math anxiety and resistance. Emphasizing a growth mindset and providing many opportunities for students to see themselves as capable problem solvers, without becoming derailed by error, is crucial. Identifying the beginnings of anxiety and resistance are also going to be key in stopping the cycle of poor math achievement. Loved your blog, I’ll be sharing this with both parents and teachers this year!
Thank you for your comment and for sharing some of the research on math anxiety. This is a fascinating area, and it’s encouraging that the body of research is growing. Renaissance is focusing on ways to make math accessible for each student. Teacher-to-teacher and researcher-to-researcher comments will build a powerful repository of information on ways to encourage the mathematician in each of us. I hope you continue to join in the conversation and share what you are finding in your day-to-day interactions with mathematics instruction and what you are finding in your research. All the best as you continue your graduate work. jb
I enjoyed reading the article about inherited vs. learned orientation in regards to math. For me, math has never been a subject I either enjoyed or exceled at, but I learned to get by with what I needed to graduate and go on to college. I do agree that a lot of one’s ability toward a given area is innate, but it does make me feel encouraged to learn that much of it too is not. I feel strongly that great and not mediocre math teachers make a huge difference along the way in school especially for students who are not more mathematically inclined. They need to know how to teach and reach those students and not just those who get the lessons and concepts the first time. Those early math experiences especially in elementary school are the foundation to a successful future in math for many kids, but secondary math teachers have to be there to encourage, teach, and build on those skills to ensure continued math growth and success.
I think a better way of looking at this issue is through parameters. Just as it is impossible for any basketball player to play in the NBA, it is impossible for any human to attain a very high level of mathematical prowess. I for example, loved basketball and practiced diligently, but succeeded in raising myself to a level of incompetence that would bemuse the average sports guy. Luckily, I was capable of being a bit better at math. Or was I? I came to math teaching during the early 1980s, when any capable math teacher was working for industry for a much bigger paycheck. Maybe I have just been lucky. But you do not have to be a math genius to recognize the genius of math, and to impart that wonder to students.
Still, we need to recognize that there are vast differences between ability levels in math just as there are in sports. Presently, under the idea that “everyone can learn” we are asking some children to proceed through their journey much too quickly. Modern testing and curriculum design is forcing teachers to introduce topics to students for which they are not prepared, exaggerating the self-evaluation that they are not “math people.”
Want to help out? Destroy all high-stakes tests and make tests informative rather than punitive.
Excellent post. 100% agree that over-testing is negatively impacting quality instruction.
I love your comment, “You do not have to be a math genius to recognize the genius of math, and to impart that wonder to students.”
I have a diverse group of 5th graders this year. One in particular is dyslexic. I don’t see the reversing of numbers at all. Her knowledge of multiplication facts is low. Could that be because of dyslexia? She tells me it is hard. I want to know more about how to help her. Your article gave me an idea. I am going to ask her to tell me the steps of division as she writes it down. Maybe talking like a math teacher may help her memory of the steps. What do you think?
Thank you, Belinda, for your comment and your commitment to this student.
When it comes to dyslexia, I would refer you to an educator with deep knowledge of those challenges. I hope you keep researching the connection, because what you learn will be of benefit to other educators. The strategy you developed to have the student talk through her division process is right on target. You may want to explore Karin Hess’ work in depth, and you can start with her recorded webinar on meeting new math standards. She offers actionable commentary about what teachers learn from students’ talk about math.
Your most direct pathway to conquering your student’s multiplication challenge is to explore her most basic math fact fluency and automaticity. She may be struggling with multiplication facts because the addition facts are not yet fluent and automatic. A recent post from Dr. Gene Kerns offers more about power of math facts fluency and automaticity. You may also want to explore what other educators have learned about math fact fluency and automaticity here.
Thank you again for your determination to accelerate learning for each and every student.
All the best,
Jan Bryan
I love teaching math and yet as a student, I was not good at math. I was fearful of teaching math until I took a continuing education class that totally changed my feelings toward math. I learned basic ideas that made so much sense that I knew I had been given the tools with which to develop a love of math for my third grade students. Every year I have students who tell me that they thought they were bad at math or hated math but now it is their favorite subject. I wish all teachers could have experienced a class with a teacher as good as what I had. After all, teachers can only teach what they’ve been taught.
All said, I have to agree with Roy Turrentine’s post. Students have differing ability levels. The current math pacing guide that I must follow does not allow for remediation periods. I work very hard to manage small groups and programs like AM to deliver individualized instruction. Too many times I feel like we are in the “I Love Lucy” chocolate scene with the students having the next new concept being shoved down their throats before having had time to digest the one that came before.
Roy’s point about high-stake testing is true. I loose 6 weeks of math instructional time because I have to test students on a one-on-one basis for reading. Yet the amount of math we must deliver in that time frame is not adjusted. Therefore, the number of new concepts they must learn gets crammed into a shorter period of time. This cycle creates students who falsely identify as “not being good at math” when all they need is more time to dig down and explore foundational concepts.