The Status of High School Mathematics: The 2018 NSSME+ Report
By David Bressoud @dbressoud
Roughly once every seven to eight years since 1977, Horizon Research has conducted a survey of K-12 science and mathematics teachers, principals, and district personnel in the United States. The latest of these studies, the National Survey of Science & Mathematics Education (NSSME), was run in 2018 with funding from the National Science Foundation. The reports came out this past spring. Full details and products from the study can be found at horizon-research.com/NSSME. The specific report I am writing about this month focuses just on high school mathematics can be accessed here. (Hayes 2019).
The report has three classifications for high school mathematics courses: Informal Review (below Algebra 1). Formal Required (at level of Algebra 1 and Geometry), and Formal Advanced (Algebra 2 and above). One striking finding is that while historically underrepresented students constitute 38% of all high school students, they make up 54% of the students in Informal Review, 39% of the students in Formal Required, and only 32% of the students in Formal Advanced.
We still have 9% of high schools that do not offer a course at the level of Algebra 2 and 10% that do not offer a course equivalent to precalculus or Algebra 3. Only 72% offer any courses that might qualify for college credit. Just over half, 53%, of high schools offer any AP Calculus, although 83% of students do have access to an AP Calculus course. IB Mathematics courses are offered in 4% of high schools, with 9% of high school students having access to an IB Math course.
The report contains a lot of interesting information about teacher preparation, beliefs, and practices. I will restrict the remainder of this column to what they learned about teachers of the Formal Advanced courses. NCTM recommends that high school math teachers have taken college courses in seven subjects: calculus, abstract algebra, geometry, discrete mathematics, number theory, probability, and statistics. The survey revealed that only 39% of those teaching Algebra 2 or above have taken courses in all seven subjects, although 83% have taken courses in at least five of those courses. The courses least likely to be taken are number theory (63%) and discrete mathematics (67%).
The big push toward statistics in high school has resulted in 91% of these high school teachers having taken a statistics course. And yet, only 34% of the teachers consider themselves very well prepared to teach statistics, and a dismal 25% consider themselves very well prepared to teach discrete mathematics. These low percentages reflect the fact that both of these courses are outside the traditional preparation for calculus. On the other hand, 93% consider themselves very well prepared to teach algebraic thinking, with 92% very well prepared to teach functions.
Most of these teachers hold enlightened views of teaching: 95% agreed with the statement
“Most class periods should provide opportunities for students to share their thinking and reasoning.”
A strong 84% agreed that
“It is better for mathematics instruction to focus on ideas in depth, even if that means covering fewer topics.”
Only 29% agreed that
“Teachers should explain an idea to students before having them investigate the idea.”
Regarding what actually happens in the classroom, the following table pulls out some of the practices that teachers reported using at least once a week. I do find it interesting that while 73% of classes have students work on challenging problems at least once a week, only 64% have students figure out what the challenging problem is asking(Table 1).
The questions about teacher control over curricular and instructional decisions showed how little control most teachers have (Table 2).
On the other hand, while commercial textbooks continue to be the primary instructional resource (for 93% of classes), only 64% of teachers base their instruction on the textbook at least once a week. Much more common (81% of classes) is instruction at least once a week based on units or lessons that the individual teacher has created. Beyond textbooks or other printed materials, 20% of classes rely on access to free websites at least once a week, 12% to websites that have a subscription fee or per lesson cost. This is not for lack of access to computers; 87% of classes report adequate access to instructional technology.
Regarding homework, 37% of the Formal Advanced courses assign less than an hour of homework per week, 29% assign between 60 and 90 minutes, 17% assign 90 to 120 minutes, and only 16% assign more than two hours per week.
The NSSME reports provide a rich source of information. I have only illustrated some of the aspects of their reports on mathematics. They have also studied biology, chemistry, physics, and computer science instruction.
Hayes, M. L. (2019). 2018 NSSME+: Status of high school mathematics. Chapel Hill, NC: Horizon Research, Inc.