Gender Bias in Mathematics

My latest issue of Mathematics Teacher arrived in the mail a few days ago.  One of the first articles, "Staring Down Stereotypes," gave several examples of stereotypes about mathematics:

• Men are better at mathematics than women.
• Mathematics requires only logic, not intuition.
• Mathematics is not creative.
• There is a best way to do a mathematics problem.
• Mathematicians do problems quickly, in their heads.
• Mathematics requires a good memory.
• Some people have a "math mind," and some don't.

The article also mentions Harvey Mudd professor Rachel Levy and her blog "Grandma Got STEM," which confronts the stereotype implicit in the direction to write an explanation to a math problem so simple that your grandmother could understand it.  The blog is a tribute to grandmothers in STEM fields and includes biographical information as well as many historical pictures.

The blog has a picture of the women from Bletchy Circle, including a link to an interview of Joanna Chorley, one of the women who worked there.  It also has a great collection of links including this interview with Eleanor Kolchin in the Huffington Post.  She was a programmer in 1946 and shared what it was like to work for IBM at the time.  She had to get married secretly because she would have been fired by company policy at the time.

The blog is inspiring, and proves that talent in mathematics and science is not confined to the young, or to men.  My own grandmother used to say to my two sisters and me, "Don't settle for a job serving a man - like a secretary.  Be an engineer or a doctor or a lawyer."  Her message was meant to convey that we could do anything we wanted.  My older sister is a computer programmer, I am a math teacher, and my younger sister went into the IT field.  Thanks grandma!

What I am Learning about Differentiating for Equity

I do not have a lot of diversity in my college classrooms.  This semester, I have 88 students total, and 6 are students of color.  I have never been challenged to differentiate instruction for equity by my division or even by the administration.  I am a novice in the area of differentiating, especially in relation to diversity or equity.  I have been learning a lot this past week by reading through recommendations made by school districts, entire states, and individual teachers.  Most of what I have read is written to the K-12 world, but could extend into the college classroom.

Mark Ellis argues in Chapter 1 of the book Mathematics for Every Student: Responding to Diversity, Grades 6-8 that "differentiation is to vary one's actions as a teacher to meet the needs to students."  (p.10).  He argues that the focus is on changing instructional practices, "moving beyond the standard, or normative, habits that characterize mathematics teaching (e.g., teacher-led lecture and demonstration followed by individual student's work on rote procedures)." (p.10)  He argues that the alternative understanding of differentiation in which the curriculum is changed in response to students' abilities should be avoided, especially in "school mathematics, with its history of providing inequitable access to content on the basis of perceived ability." (p.10)

I read another succinct way of describing differentiated instruction in a document by the Metropolitan Center for Urban Education called Culturally Responsive Differentiated Instructional Strategies: "Through differentiated instruction, students will get to the same place, but take different paths." (p. 2)  So culturally responsive differentiation is not watering down the curriculum for some students, or even individualized instruction.  "Differentiated instruction suggests teachers look at “zones” in which students cluster so they can offer three or four routes to a goal on a given day." (Culturally Responsive Differentiated Instructional Strategies, p. 3)

I also came across a Research Brief titled "Increasing the Achievement of African American Males" which was a report from the Department of Research, Evaluation, and Assessment in Virginia Beach City Public Schools.  The report detailed factors that contribute to the achievement gap of African American male students, and suggested strategies aimed at improving their achievement.  The report stated on pages 5 and 6:

Culturally responsive instruction pertains to classroom practices that draw meaningfully on the culture, languages, and experiences that students bring to the classrooms in order to increase engagement and academic achievement for students of color (Au, 2006; Ladson-Billings, 1995).  A few of the most common tenets of a culturally responsive pedagogy included (1) acknowledging that valuable knowledge resides in students’ home languages and cultures and that this home knowledge is not always valued in the schools; (2) pursing academic success for students of color; (3) creating valuable connections between students’ home and school experiences; and (4) fostering social justice (Dutro, Kazemi, Balf, & Lin, 2008).

One way in which I can implement these tenets is to spend the time getting to know my students' native language and culture.  I each lunch on campus everyday and I value that time to connect with other professors and staff members on campus.  However, I can also take the time to connect with students of diverse backgrounds.  I recently had lunch with an international student who was born in China but grew up in Italy due to her parents' jobs.  She explained some of the differences between Eastern and Western culture that she has encountered in her education.  She helped me understand some of the challenges that international students face.  In order to provide effective culturally responsive instruction, I need to become more familiar with the experiences and backgrounds of my students, and this will require spending time with them outside of the classroom.

The report also listed characteristics of effective African American teachers on page 10:

In his work, (Howard, 2001) assessed three major culturally responsive strategies used by highly qualified African American teachers who taught mainly African American students. Holistic, culturally communicative, and skill-building were the three strategies discussed in his study. In essence, the report emphasized that culturally relevant teachers are personally warm toward and respectful of, as well as academically demanding of, all students.

Holistic strategies recognize that not only the intellectual, but also the social and moral capabilities of students need to be developed.  This involves teaching students "character building, honesty, responsibility, respect, cooperation, sympathy to others, and behaving in ways that are consistent with the social norms of the classroom and society." (p.10)  At a Christian institution, these holistic strategies fit into the goal of developing the whole person, not just the mind.  I usually only have students for one semester in my classes, but once I am finished with my master's degree and have more time to connect with students, there are mentoring opportunities available.  In fact, there are mentoring opportunities available at my son's middle school (grades 7 & 8) and also with an organization called Urban Transformation Ministries that my church is connected to in which I can help to encourage students of color.

Culturally communicative strategies take into account the language patterns of students.  The report gave an example of this on page 10:

According to one teacher, students “talk all day in class and don’t get focused, but if you give them leadership roles of leading a group or leading a class discussion, they are very successful” (Howard, 2001, pg. 190).  

The report mentioned that teachers took into account that many African American students prefer oral rather than written expression, and gave an example of having students listen to a story before writing about the story.  I need to provide opportunities for students to express their mathematical knowledge orally, both in class and on assessments.

Skill-building strategies recognize that all students have the ability to think, or are "smart", but that some students have developed more skill.  This aligns with the ideas from the Mindset book we talked about earlier in the semester.  These ideas can help counter the cultural myths that some students just can't do math.  I can talk about these ideas at the beginning of the semester, and refer to them whenever I encounter the fixed mindset in students.  

Another related quote from Mark Ellis in Mathematics for Every Student: Responding to Diversity, Grades 6-8 about working with a 7th grade student named Alonso:

Although I realized that he lacked proficiency with many mathematical concepts and skills, I did not equate this lack with Alonso’s having a low ability to do mathematics.

I think that sometimes it is difficult to see students who have lower math skills when entering our class as equally capable of doing math, but I believe that it is critical in addressing the inequities that are present in our culture.

I am still at the beginning steps of differentiating in culturally responsive way.  I can make progress toward better understanding the students in my classes who have a cultural background different than my own, affirming their ability to learn mathematics, and providing alternate paths to achieve success.

5 Practices for Orchestrating Productive Mathematics Discussions

I teach three sections of College Math every semester - usually one right after the other on MWFs.  I usually have about 100 students in total.  While teaching the same class three times a day can sometimes be challenging (I always hope that my most talkative class is last), it has given me momentum to improve the class each semester.   Usually there are five sections of College Math each semester and I collaborate with the two adjunct professors who also teach the course.  Last year these colleagues and I started experimenting with the flipped class.  Our motivation was the desire to have more class time for discussion and application of the knowledge that students were learning.

One example is the lesson on measures of central tendency and measures of variation - mean, median, mode, range, five-number summaries, and standard deviation.  We usually had to spend a significant portion of time reviewing how to calculate these measures and ran out of time to analyze when to use them or what they reveal about sets of data.  So I created a video explaining how to calculate these measures and assigned watching it and filling out guided notes as homework due before class.  During class we spend time discussing when to use each measure and how to interpret what the measures are saying, especially in comparing sets of data.

I realized pretty early on that I needed to learn how to structure the flipped class time differently and that I easily slid back into a lecture mindset on those days.  I have not experienced a math class as a student where discussions are the central format, nor did I learn how to facilitate mathematical discussions in my teacher preparation program in college.  Since I was able to choose the topic for a project in my current grad. school class, learning about how to do this better seemed like the obvious choice.

I just finished reading a book by Margaret S. Smith and Mary Kay Stein called 5 Practices for Orchestrating Productive Mathematics Discussions, recommended to me by my professor.  I learned so much from this relatively short book.  Here are some quotes:

"In mathematics classrooms, high-quality discussions support student learning of mathematics by helping students learn how to communicate their ideas, making students' thinking public so it can be guided in mathematically sound directions, and encouraging students to evaluate their own and each others's mathematical ideas." (p. 1)

"Teachers often think of lessons in relation to the activities that they will ask students to do rather than what students will come to know and understand about mathematics as a result of having engaged in the lesson." (p. 15)

"I must consider the mathematics in relation to the children and the children in relation to the mathematics." (p. 50)

"What students learn is intertwined with how they learn it." (p. 61)

"Almost all good classroom discussions begin in the same way: by inviting a student to share how he or she solved a particular problem.  After the initial student response, however, classroom discussions diverge--separating into the relatively rare fruitful ones and the much more frequent unproductive show-and-tells.  It turns out that issuing an invitation to students to reveal their thinking is a relatively easy thing to learn how to do.  And most students will comply......Typically, however, teachers treat all presentations as equally good, they ask few questions of the students, and they do not connect different student presentations with one another or the disciplinary ideas under investigation." (p.69)

This book lays out five practices designed to remedy this situation:

1. Anticipating - considering ahead of time how students might approach a mathematical task, both correctly and incorrectly, and how those relate to the things that a teacher wants students to learn
2. Monitoring - paying close attention to students are they are working on a mathematical task and keeping track of strategies used as well as asking questions of students to help guide their thinking and keep them engaged
3. Selecting - picking particular students to share their work in order to get certain mathematics into the open for examination by the class
4. Sequencing - purposeful ordering of the student work being presented so as to maximize the chances of achieving the goals for the lesson
5. Connecting - drawing connections between the student work that is presented and the key ideas of the lesson

A necessary foundation  for these practices to be successful is setting clear goals and selecting tasks that are conducive to discussion.  The goal of the lesson needs to clearly identify what students should know and understand about mathematics and consequently will guide the selection of appropriate tasks.  The tasks need to be of sufficient depth to stimulate and provide opportunity for discussion.

I also appreciated the chapter on asking good questions and keeping students accountable for their understanding of the material.  Here is a list of questions asked by teachers in various classroom scenario presented in the book:
"What does this mean?"
"Why did you do it that way?"
"Can you explain more to me about that?"
"Does anybody want to add to that?"
"How do you know that?"
"Do those two things mean the same thing?"
"Does everyone agree with this?"
"Is there another way?"
"Can you repeat what [insert student's name] did to solve this?"
"How can we know for sure?"
"Can you always do that?"

The value in these practices is to provide a structure that will help transform class discussions from a "show-and-tell" format to an intentional interweaving of student work with the mathematical goals of the lesson.

The next step is to implement these five practices with a lesson in the College Math class that I teach, involving the adjuncts along the way.  Collaboration will improve the process.  Let the project begin!