When Janet Johnson tried to enroll in advanced courses, her high school counselor told her that those courses were for students who were going to college. The school counselor explained that students must be invited to enroll in those courses, and she had not been invited. The school counselor told her that she was “not college material.”
Although blocked from enrolling in advanced courses in high school, I still planned to go to college. I worked at the Dairy Queen, babysat, and detassled corn and saved all my money. Although I had a very high ACT score, received a letter from the Governor of the state congratulating me for being in the top percentile, and had always been on the Honor Roll, I did not apply for any scholarships. I did not know about them. A friends’ mother gave me an application to the state college her daughter planned to attend. This was the only college that I applied to, and I knew nothing about it. I was accepted and attended for one semester. Then I was out of money. I had given it my best shot. I had worked hard all though elementary, middle, and high school and earned very good grades. I had saved money for years. I was out of options. I left college and went back to my hometown and became a waitress.
After being a waitress for several years, I worked my way from a coffee house up to the local private golf club, where I could make a decent living and had benefits. I then became the head waitress at an even nicer restaurant in my hometown. I was tutoring a friend in math, who was attending the local liberal arts college, Knox College. Seeing how easy the math was for me, he wondered why I had not attended college. I explained that I had, but I ran out of money. He urged me to apply to Knox College, and to apply for a scholarship. I thought scholarships were for athletes or for people with musical talent. Much to my surprise, Knox College offered me a full scholarship for a female to major in math. I kept working 40 hours a week as a waitress while attending Knox and majored in math. I got a teaching certificate for good measure. I always enjoyed tutoring math and trying to explain things in ways people would understand.
Although I loved to teach, I also loved math. I went to graduate school at Northern Illinois University and studied non-commutative ring theory (with John Beachy) as a concentration. I loved learning this math and it made perfect sense to me. It helped me understand structures and how to interpret things. I started to view the math I already knew differently. I could see how concepts built on each other in ways that I had only understood as procedures in the past. I thought math would be much more consumable to others if they could see how concepts related, but many of these relationships were only taught to graduate math majors.
I had gained a reputation for helping people get through college math courses. Several friends I grew up with came to me for help getting through math courses required for their graduate degrees. I became curious as to why these very bright, hard-working people needed help with very basic math. I developed the theory that they had been taught math as complicated procedures to memorize, and were never taught the underlying concepts. I could see that many people believed that some people have math brains and others don’t. I believed that most anyone could understand math if the underlying concepts were explained.
Teaching Math in a Magnet School
I got a job teaching math in a magnet school. I had never heard of a magnet school. This was a Math/Science magnet. The students were children of the university folks and children from the projects. Math course placement was based on demographic information. The Caucasian children of the university staff were in the advanced math track. I taught all the 8th grade math classes. I could see that students’ prior math scores and demonstrated mastery were not used for math placement.
I was given different books and different curriculum for each track. Just as I had begun to suspect, the books for the lower track taught rote computational skills. The books for the upper tracks taught underlying concepts. The chapters in the lower-track texts weren’t even organized so that concepts built on each other. This confirmed what I had suspected, and explained why very intelligent students who were not in the top track knew almost no math. They just memorized things, and all topics were stand-alone. I disregarded the books and taught students the concepts underlying the procedures. I supplemented the curriculum with Math Counts material. I had Black, female, and low-income White students on my First Place Math Counts team.
My eyes were opened when I was to place these students into their high school math classes. I placed all the Math Counts winners into advanced math in high school. I was told I couldn’t. I was taking too many slots in the advanced track. When I explained how important it was for these kids to be in the top math track (now that I had seen the standard track), I was finally told, “You don’t get it. We have to take care of the kids whose moms bring the Teacher Appreciation Breakfasts, and run our PTA, etc.” This is when I realized how it works. And why I could not take college prep in my high school.
I loved mathematics, and I had become very interested in math education. I now believed more than ever that most anyone could learn math if taught the underlying concepts instead of being expected to memorize stand-alone procedures. Having seen how math placement was primarily done demographically, and the different curriculum for the different tracks, I came to believe this in large part created the achievement gaps in math. I entered the math education Ph.D. program in NCSU and had the privilege of studying under the young professor, Dr. Lee Stiff.
I noticed that many math educators believed that the students who are not in the top math track are weak and unable to comprehend math concepts. Many even got upset when I would suggest otherwise. They seemed to enjoy being in what they understood as a special class of people who were able to learn math, while most people are not. Dr. Stiff and I both firmly believed that with proper instruction, most students could understand mathematics.
After I graduated with my Ph.D. in math education, and minor in statistics, I worked for a large NC school district doing research on effective programs, and accountability for federal grants. I heard a lot of talk about wanting to close achievement gaps, but I also saw services and course placements being done primarily by demographic characteristics in lieu of achievement scores.
I later started a small business to help school systems work with data, conduct research, and do program evaluations. About 2006, the school counseling department of a large district asked me to help them use data to determine who drops out of school and effective ways to close achievement gaps. We analyzed the data for this entire school system and saw that thousands of minority students who had scored the highest possible levels on mathematics achievement tests were enrolled in standard and remedial math courses. When the school counselors tried to enroll these students into advanced courses, they were met with the same types of resistance that I encountered when I enrolled my first place Math Counts winners in the advanced math courses a decade earlier. We worked with some principals who used this data and moved these top scoring students into advanced math classes. We saw achievement gaps close in one year, as a result. We also saw the tremendous push-back that occurred. Dr. Stiff and I wrote about this and published in peer-reviewed journals (Stiff & Johnson, 2011; Stiff, Johnson, & Akos, 2011).
Dr. Stiff and I began advocating for equity and inclusion in advanced math. Although we both believed that nearly anyone can learn advanced mathematics if taught well, we advocated for at least allowing students who have already demonstrated mastery to enroll in advanced mathematics, as a start. The resistance to this was massive.
In addition to being told that high scores on math exams do not indicate potential to learn advanced math, Dr. Stiff and I were also told that it makes no difference when a student takes algebra–in 8th or 9th grade. Math educators know that students who take algebra in middle school are on a path to take rigorous math courses in high school—a path that other students do not have access to. So, we ran a statewide analyses of the data, working with both SAS and NC Association of School Administrators (NCASA), to compare top scoring students who took algebra in 8th grade vs. 9th. Level 3 students who took 8th grade algebra were 55 times more likely to take chemistry and physics than similar students who took 9th grade algebra, and almost no one ever went into the Honors track from 9th grade algebra—no matter how well they did. (This is because 9th grade algebra teaches the students as if they are weak and can only memorize procedures, while 8th grade algebra prepares students to understand math and be able to learn science.)
Dr. Stiff and I have made a great team, with my analyses of the data and his inspiring speaking skills. We have been working together for almost 30 years to convince people to have high expectations for all students, and to allow low-income and minority students into advanced math. https://www.youtube.com/watch?v=RRsv_rwZkyw . We coined the term “Pro-Equity Model” to replace the “At-Risk Model.” We have worked together to try to change the way people view mathematics, and to promote equity in access.
NC Math Access Policy
NC now has legislated that students who score the highest possible score must be given the most enriched math lessons. This is to start in 3rd grade.
In our work with schools all over the state, we are finding that many elementary schools have been providing enriched math lessons to students who have been labeled Academically or Intellectually Gifted (AIG), and only to them. The school day isn’t set up to make it easy to provide these lessons to students who are not labeled AIG.
We know both from our work, and from Implementing HB986_Presentation from NCDPI_April 2019, a presentation given by the North Carolina Department of Public Instruction, that nearly half the students in the advanced math did not score at the highest level, and some even score at the lowest level. This law will only give access to those overlooked who scored at the highest level. It’s a start.
We also know from the News & Observer series, Counted Out, that low-income students are not as likely to be labeled AIG as academically similar non-poor kids. And, there is no real definition for AIG. It differs across school systems.
BEST-NC has done a great job of raising awareness, advocating for children, and providing information.
Stiff, L. V., & Johnson, J. L. (2011). Mathematical reasoning and sense making begins with the opportunity to learn. In M. E. Strutchens & J. R. Quander (Eds.), Focus in high school mathematics: Fostering reasoning and sense making for all students (pp. 85–100). Reston, VA: National Council of Teachers of Mathematics, Inc.
Stiff, L. V., Johnson, J. L., & Akos, P. (2011). Examining what we know for sure: Tracking in middle grades mathematics. In W. F. Tate, K. D. King, & C. R. Anderson (Eds.), Disrupting tradition: Research and practice pathways in mathematics education (1st ed., pp. 63–75). Reston, VA: National Council of Teachers of Mathematics, Inc.