Marissa’s hurt brown eyes looked unhappily at me across the class full of eighth-grade math students.

Surprised, I asked myself, What did I say? I mentally replayed my last comment. A building contractor uses functions as he plans building projects with the same house design.

He. It suddenly hit me. My poorly worded example had completely excluded Marissa—and half of the class. Marissa knew it, and her eyes communicated her dismay. I immediately corrected my pronoun use, noting that both women and men can be contractors. Relief washed vividly over Marissa’s face, and I made a mental note to talk with her later.

Mathematics is my love and my passion. I’ve been a mathematics educator for thirty-five years, and a consultant for more than twenty of those years. I’ve dedicated my life to helping all students find their genius for mathematics, their own passion for math, and their voice to claim their place in classrooms and in life.  So how could I fall into the same trap that I have talked about so many times with groups of teachers?

In “Debunking Myths about Gender and Mathematics Performance,” Jonathan M. Kane and Janet E. Mertz share some answers to my question. Differences in boys’ and girls’ rates of participation in mathematics and the small differences in their levels of performance are most likely due to “a variety of sociocultural factors present in their environment.” Specifically, the authors note that equity in society, employment, and pay correlates to the socioeconomic status of the home. The article states that “well-educated women who earn a good income are better positioned to ensure that their own children’s educational needs are met.”

As I read the authors’ conclusions, I reflected back on my experiences as a child. How did I ever become a mathematics author and consultant? Surely good fortune smiled on me, because the sociocultural factors present in suburban Tucson, Arizona, in the 1960s and 1970s most certainly did not.

I remember my beloved third-grade teacher answering my question about the procedure for adding fractions with, “Don’t ask why, Christy. Just do it.” I was a good little girl. So I stopped trying to make sense of math.

I remember my conscientious sixth-grade teacher worrying about too much stress in junior high, and recommending that Jimmy, who also got all As, take high math and average reading. I, a girl, should take average math and high reading, he decided.

So in seventh grade I found myself in a classroom with students who were practicing their multiplication tables, which I had learned years ago. My schedule didn’t get changed until the spring semester, when I finally joined the high math class. I struggled for the remainder of the year, having missed an entire semester of learning. This one event impacted my choices for the rest of high school and college.

I remember that, as a sophomore in high school, I consciously chose wrong answers on a standardized test, to try to gain the acceptance of my peers who looked down on “those smart kids.”

I know that the world of today has shifted profoundly in many of its assumptions about girls and math. However, the specter of old habits and words—and even beliefs—peers out from the shadows, anxious and ready to hop out at a moment’s notice, eager to recreate yesterday’s culture.  Just as I did, we teachers invite that ghost from the past into the present through our words and misstatements. How often do teachers say that they’re not good at math, unwittingly giving permission for their students—especially the girls—to give up? How often do teachers forget to highlight that success in math is the key to opening doors in college and careers?

Girls need chances to use mathematics in the games that they play, by building with blocks (not just the pink and purple ones), and through mental math (I occasionally invited my daughter to keep the change if she could figure it out before we got to the cashier). Girls need to learn that they are good problem-solvers, that they can justify their thinking, and that math is an exciting, vibrant tool for making sense of the world. Girls need to see mistakes as learning opportunities, and success as a cause for celebration.

I sincerely hope that Marissa stays in the game of mathematics, that she develops confidence born of solid skills. I hope that Marissa can continue to challenge unthinking remarks such as mine—not only with her eyes, but by raising her hand to question them—knowing that she has the solid support of her peers. I pledge to continue to do my part, to remain vigilant, to make sure that “math is for boys” becomes “math is for everyone.”

Research studies and news media articles about the gender differences in mathematics achievement are prevalent and still at the forefront of debates regarding education in our society. Most recently, Kane and Mertz’s 2012 article, “Debunking Myths about Gender and Mathematics Performance,” has received a lot of media and social network attention.

As a mathematics educator, I expect and hope to see both genders do well in mathematics, and I strive to help every child reach her or his potential. Because I believe in every child’s ability to learn mathematics, what concerns me is that schools continue to report girls’ low enrollment numbers in elective math and science classes. More often than not, high school teachers indicate that their advanced math, engineering, and elective physics classes are disproportionately populated with boys.

Where have all the math girls gone?

What is it about these classes that are attracting more boys than girls? What are girls choosing to take instead of math and science classes? As an elementary mathematics teacher and coach, I have observed female students not only enjoying mathematics and science but also demonstrating aptitudes parallel to the male students and developing deep (and, I hope, lasting) interest in math and science. Yet the statistics predict that these girls who are interested in math and science are likely to be underrepresented in such elective and/or advanced courses at the secondary level. Why aren’t they signing up?

I wonder if the stereotypes about girls not being good at math affect female students more than we realize. If this conjecture is correct, by the time these females reach high school, no matter how much they might have loved math in elementary school, they opt not to participate in math and science classes beyond the requirements. Krendl et al. (2008) conducted a study using neuroimaging to see what happens to the brain when a person is confronted with a stereotype. They found that women who were told that “research has shown gender differences in math ability and performance” (reminding women of gender stereotypes in math ability) underperformed on the math problems they were given. The neuroimaging showed that these women’s brains did not show recruitment of the mathematical brain regions and instead showed activity in the region of the brain associated with emotional information, whereas the women in the control group (without the stereotype threat) showed heightened activation in the mathematical brain regions and not in the emotional regions.

Since we know that . . .

* lack of gender equality in American culture is affecting gender differences in math participation (Kane and Mertz 2012),

* many girls are opting not to sign up for higher-level math and science classes, and

* stereotype threat not only produces anxiety toward mathematics but also can affect achievement in mathematics (Krendl et al. 2008),

. . . then I am wondering if developing students’ sense of agency in mathematics could potentially combat some aspects of gender gaps in mathematics and science. Lately I’ve been thinking a lot about the role of self-efficacy and developing a sense of agency in learning. I recently revisited one of my favorite books, Peter Johnston’s Choice Words: How Our Language Affects Children’s Learning, and reflected on how we as teachers play a critical role in developing students’ sense of agency. Johnston writes about building agency around successful events and says that, in school, “It is our job to help expand the possible agentive narrative lines available for children to pick up” (2004, 40). I think it is important to talk with girls about the gender stereotypes that they may run across and how these have the potential to impact girls’ own narratives about their math abilities.

Could this development of “agency” be a factor in encouraging more girls to continue to develop their interests in mathematics and science? If developing agency is a critical part of combating gender stereotypes, what are the implications for our teaching? What are the best approaches to developing students’ sense of agency, especially in light of gender stereotypes and inequalities that are still present in society?

References

Johnston, P. H. 2004. Choice Words: How Our Language Affects Children’s Learning. Portland, ME: Stenhouse.

Kane, J. M., and J. E. Mertz. 2012. “Debunking Myths about Gender and Mathematics Performance.” Notices of the American Mathematical Society 59(1): 10–21.

Kendl, A. C., J. A. Richeson, W. M. Kelley, and T. F. Heatherton. 2008. “The Negative Consequences of Threat: A Functional Magnetic Resonance Imaging Investigation of the Neural Mechanisms Underlying Women’s Underperformance in Math.”  Psychological Science 19(2): 168–175.

I have been working on writing this post for more than a month and have written it many times only to immediately delete it. Each of these attempts has been preceded by hours of thinking about performance by gender during the wee hours of the morning, when it is dark and quiet and no one is awake to interrupt my thoughts. I have come to the conclusion that gender is not really the issue—the issue is bigger. In fact, the issue involves ALL children and how to help each one reach her or his greatest potential.

Do boys outperform girls in mathematics? Research is available to support various opinions on this matter. Although it is important that girls do well in mathematics, it is just as important that ALL students perform to the best of their ability. Gender, intelligence, primary language, socioeconomic level, and so forth should not be factors or challenges to a child’s opportunity to reach her or his potential in mathematics or any other subject area.

What is success in mathematics? I define success as moving forward in the acquisition of knowledge and understanding and the ability to apply it to new learning and problem solving at a speed that allows for deep understanding but doesn’t stagnate the learner. Rather, the learner remains engaged, excited, and interested.

What are the characteristics of successful learners? In my experience as a practicing public elementary school teacher in grades pre-K–6, successful learners do the following:

• Persist
• Possess self-confidence
• Are open to new learning and ideas
• Work to make sense of situations and their learning
• Make connections
• Reflect on solutions to be sure they make sense, and revise when they don’t
• Ask questions and put forth ideas and hypotheses
• Listen to others and discuss ideas and solutions
• Apply what they know to solve new problems
• Communicate their ideas through speaking and writing
• Use a variety of tools including paper and pencil, manipulatives, calculators, charts, graphs, computers, etc.
• Search for and make use of patterns and structure

Although successful students display a common set of learning attributes (as listed), these students come in all varieties: gifted, special education, English only, English language learners, rich, poor, Hispanic, black, white, Native American, Asian, female, and male. Success in my third-grade classroom is not limited to boys or any other particular group.

How then do we create classrooms where all students perform to the best of their ability? There seem to be two key areas where we, as classroom teachers, can make a difference. These areas are: (1) our beliefs about our students and their abilities, along with our role in helping them to achieve success, and (2) the opportunities we provide.

• Beliefs: It is imperative that we hold high expectations for our students as well as ourselves. When people truly believe they can do something, they will do it. The same is true when it comes to learning mathematics. I believe that all of my third-grade students can understand the concept of multiplication, and it is my job to find ways to make this happen for them. It is also my job to convince them that they are capable of understanding. As students rise to meet my expectation for understanding multiplication, they develop self-confidence, which enhances their belief that they can achieve. When students believe they are capable, know that I believe they are capable, and have experience with success, they will persevere. They will make sense of their learning and apply it to new problems and situations, and in new ways. Asking ALL children to share and discuss ideas, in writing and aloud, values their thinking and further strengthens an “I can” attitude.

There are cultural values that we have to watch out for that can be confusing to students. For example, when adults make lighthearted comments such as, “I was never good in math,” we need to be prepared to respond. Adults usually do not make such comments about their abilities in reading, so why is it okay to make such confessions about math? It conveys the message that it’s acceptable not to do well in math.

• Opportunities: Because each student is unique, we must provide learning experiences with multiple access points and ways to extend learning. Learning opportunities need to accommodate different learning styles, interests, and skill levels. Students must have opportunities to demonstrate their learning in multiple ways. Opportunity for students to reflect on their learning and revise when appropriate is essential. They need opportunities to make connections and explore ideas. Students need many different opportunities to engage with and explore a single concept. Mistakes are not failures; they are golden opportunities to learn. We should all be expected to learn from our mistakes.

To sum up, not only do we need girls to do well in mathematics, we need ALL students to reach their full potential.

The topic has been in the news lately with several studies and blog posts circulating among parents and educators.

Researchers Jonathan Kane and Janet Mertz set out to answer the question in their recently published article, “Debunking Myths about Gender and Mathematics Performance.” Along the way, they devote statistical analysis to a range of theories that have been put forward to explain the greater participation of males in high-end math classes and math-oriented careers, including the following:

• “The greater male variability hypothesis”—I.e., boys are biologically predisposed to quantitative fields, whereas girls are more comfortable with nurturing ones.
• “The gap due to inequity hypothesis”—Girls perform worse in math in countries that have a lot of gender inequity.
• “The Muslim culture hypothesis”—In certain Muslim countries, there is little gender gap in math performance.
• “The single-gendered classroom hypothesis”—Maybe that’s because boys and girls are taught in separate classrooms in many Muslim countries?

Through their analysis, Kane and Mertz reject all of those theories in favor of what they call “the gender stratified hypothesis”—boys and girls are born with similar potential but end up displaying differences due to a complex mix of sociocultural factors, including the education and income levels of women and their ability to advocate for their children.

The researchers point out that because girls’ math performance is linked to sociocultural factors and not biology, it can improve over time, as it has in the United States during the past several decades (according to Kane and Mertz):

• Girls have reached parity with boys in math performance in the United States, even in high school, where a large gap existed in the 1970s.
• In the 1970s, boys scoring higher than 700 on the math portion of the SATs exceeded girls by a ratio of 13:1. In the 1990s, the ratio had dropped to 3:1.
• The percentage of math PhDs awarded to U.S. citizens who are girls has risen from 3% in the 1960s to 30% in the past decade.

That’s significant progress, but we still have a ways to go. We asked three of our math authors to comment on what we can do to ensure that both girls and boys reach their potential in school and in their careers. Over the next week on this blog we will hear from Chris Confer, coauthor of Small Steps, Big Changes; Jessica Shumway, author of Number Sense Routines; and Maryann Wickett, coauthor of the Beyond the Bubble series.

What is your take on the topic? Leave your thoughts in the comments section.

Small Steps, Big Changes tells the story of teachers who gradually shift their beliefs, build confidence, collaborate, troubleshoot problems, and enhance positive attitudes about math. Chris and Marco challenge teachers and administrators to become problem solvers and researchers as they build communities of mathematical excellence. And they distill “what it takes” for all students to be successful in mathematics and to sustain that success:

• setting goals that translate high-level standards such as the Common Core State Standards for Mathematics into actual classroom practice;
• creating a school culture of mathematical thinking, problem solving, and research;
• using “knowledge packages” that organize staff thinking and help students clarify and connect mathematical ideas through concepts, skills, representations, strategies, and language;
• fostering instructional habits such as embracing complexity, keeping math visible, encouraging student talk, and structuring lessons consistently.

Print copies of Small Steps, Big Changes are now shipping, and we’ve just posted the full text of the book for preview online.

On a recent visit to a middle school I had the opportunity to attend two different math classes. I walked into one eighth-grade algebra class and was overwhelmed by the buzz of excitement. Some students were working at the board, others were working on individual white boards, while still other heads were bent over the same problem with the students discussing the next steps.

It took me a moment to find the teacher in this busy classroom. I found her standing between two students at the board. She was asking clarifying questions of one student as she tried to understand what he was thinking at a particular point in the solution process. I came to discover that this teacher was using a round-robin exercise with part of her class as a means of determining how proficient her students were with solving multi-step equations. She had organized her class into groups of three and had given each student the numbers one, two, or three. She began by sending student two to the board to record the equation she announced. Student two recorded the equation and solved only the first step. Student three replaced student two at the board to complete the second step, followed by student one. This continued until the problem was solved. The teacher explained to me that by using this round- robin activity she is able to determine at a glance how well each student is able to enter into the solution process and whether or not any students display misconceptions about solving problems.

I asked some students what they thought about going to the board and was pleased to hear Luis say, “I really like going to the board and the fact that I can get help right away if I need it. I can even help my teammates. And B.J. shared his relief that they go to the board because, “I need the extra time practicing and when I work alone I don’t know if I am doing the math correctly but when I go to the board,  I get all the help I need from my team mates or my teacher.”

Next I visited another eighth-grade class and found that in this class students were grouped into triads and were trying to solve the problem Is It a Function? Each student had two clues that they had to share orally within their group to answer one question. I listened to one student asking, “What do I need to know about perpendicular lines?” A teammate responded, “I think there is something about the slopes of perpendicular lines but I don’t remember what it is. Why don’t we draw two lines that make a right angle and see what we get.” I was thrilled to hear the questions and see the strategy that this group used to make sense of the problem. Still another group was working on finding the slope of the line they had identified. They had graphed the ordered pairs given in the clues and were working on the equation. I also observed the teacher walking around listening to the groups, stopping to ask questions as she deemed necessary.

These interactive algebra classes are the polar opposites of how traditional algebra classes are run where the teacher shows and explains to students how to manipulate symbols. The students in the classes I visited actually knew what questions they need to ask to deepen their understanding. In both of these classes I was delighted to see students trying to make sense of the algebra on which they were working. These two teachers engage their students in solving rich problems. The collaborative nature of these classes illustrates just how much students can achieve when they are given the opportunities to solve interesting problems which require them to apply the procedural skills they have learned. And the teachers I observed model the positive impact effective formative assessment has on student learning.

The Xs and Whys of Algebra is an 84-page flipchart that cuts through the confusion to help you prevent common misconceptions. Following the same practical format as their popular Zeroing in on Number and Operations series, Anne Collins and Linda Dacey provide 30 modules that focus on key ideas with instructional strategies, activities, and reproducibles for:
• using variables meaningfully;
• using multiple representations for expression;
• connecting algebra with number;
• connecting algebra with geometry; and
• manipulating symbols with understanding.
All teachers of algebra should have this handy flipchart at their fingertips during planning and instruction. You can preview two of the modules—Systems of Linear Inequalities and Posing Problems for Inequalities—online now.

Kassia Omohundro Wedekind

I hope you all had a chance to check out all four blogs participating in this week’s Math Exchanges blog tour. The interviews with author Kassia Omohundro Wedekind were very interesting and in-depth and there were some really good comments and discussion.

Things kicked off on Monday at Catching Readers, hosted by Pat Johnson and Katie Keier. In their interview they asked Kassia how teachers can stay true to the idea of ”teach the mathematician, not the math,” and not solely focus on what their pacing guides dictate. “I think we, as teachers, can make a powerful choice to teach responsively, even in the difficult time in which we teach,” said Kassia. “We can show the amazing true understanding that comes from teaching a child to construct understanding rather than memorize isolated facts and procedures. We can change how people view mathematics in their lives and in the world,”

You can read the full interview here for more inspiration!

At Our Camp Read-A-Lot, teacher and blogger Laura Komos asked Kassia about what changes she should expect to see as she begins to use math exchanges with her first graders. “I think one major shift you will see is in your first graders is how they view themselves, not just as do-ers of the work their teacher assigns them, but as mathematicians,” wrote Kassia. “In a math workshop kids feel ownership over their thinking and work. They feel a sense of pride when talking about the strategies they used to solve problems. They take on challenges and see themselves doing the real, authentic work of mathematicians.”

Laura’s full interview with Kassia is here.

For Cathy Mere at Reflect and Refine, Kassia’s book was the “right book at the right time.” At the beginning of their conversation, Kassia describes how her math workshop changed when she started to focus on “teaching the mathematician.” You can find their interview here.

At Elementary, My Dear, teacher Jenny Orr and Kassia address the very important question of how to be the first or only teacher to use math exchanges in a school. “Start small. Start simly,” advises Kassia. Read the rest of her advice here.

P.S. A note about our giveaway: Each blogger will pick one commenter as the winner of a free Stenhouse blog. You will be contacted by the blogger with details if you are the winner!

Data Routine Tips, Ideas, and Questions
Assigning Data Collection Jobs
It is important to allow students some element of choice for their data collection jobs. However, for management purposes, in the beginning of the year I choose their jobs for them based on skill level and needs (they indicate first, second, and third choices, and I take their requests into account). This allows for differentiated instruction through pairings. Students who are comfortable reading the thermometer, sunrise/sunset data, and moon phases data and recording that information hold these jobs in the beginning of the year in order to get the routines going. During this time, the student I assign to be Data Assistant is often not as comfortable with these skills, but the job of Data Assistant gives him or her time to observe and learn how to do the other jobs and pushes his or her learning to an independent zone.

During the second quarter of the school year, I often flip-flop the roles. I often assign the role of Data Assistant to someone who is strong in collecting and recording the data, and that person can assist the others in learning their jobs. This pushes the thinking of all the students involved. This pairing challenges those who are not yet proficient with collecting and recording data and it challenges the Data Assistant to explain his or her thinking; the Data Assistant is not allowed to do the other jobs for his or her classmates; he or she must use words to describe what to do.

Questions for Differentiation
• What do you notice about the data? (Use an open-ended question like this to spark discussion and give you a sense of where students are in their thinking.)
• Why do you think that? (Use a question like this in response to statements such as “It’s getting colder”; you are asking
students to talk about the data and cite evidence; you are asking them to “prove it.”)
• What was the temperature on October 10th?
• What days during this month were the warmest? The coldest? The most mild?
• What was the lowest temperature this month? The highest temperature?
• What has been the range of temperatures this month? (Emphasize the strategies for figuring it out by asking How do you know?)
• What days so far this year have been warmer than today?
• How many days so far this year have been warmer than today? (Again, emphasize the strategies for figuring this out by asking, How do you know? Some students might count one by one, some might group and skip-count, some might use the number of days in school and subtract, and so on.)
• What do you think the graph will look like next month?

Summarizing the Data Each Month with Mode, Average, and Range
• What is the most common temperature this month? (Mode)
• What is the mean temperature for March? (This arithmetic average/mean question would be appropriate for some third-grade students and many fourth-grade students.)
• What was the range of temperatures this month? (This question asks about the difference between the highest and lowest temperatures.)