July 2022 Research Rundown
By Tim Essenburg
It’s time to dust off the Research Rundown—our curated list of recent, relevant research we think is worth adding to the education equity conversation—and jump back into some data. This month, we’re sharing research on elementary mathematics, including:
- Teacher preparation program evaluations,
- The correlation between student math anxiety and achievement, and
- Math anxiety among elementary educators.
Teacher Prep Review: Preparation for Teaching Elementary Mathematics
National Council on Teacher Quality, May 2022
Across the nation, more than 1,500 four-year colleges and universities grant certificates, undergraduate, or graduate degrees in education. Through its Teacher Prep Review, The National Council on Teacher Quality (NCTQ) periodically reviews program quality based on several standards, including admissions, classroom management, and program diversity. NCTQ’s latest review explores trends and recommended practices in Elementary Math Preparation. The organization assessed more than 1,100 teacher preparation programs (TPPs) using data from course catalogs and syllabi—and they gave each a letter grade (A to F) based on a standardized rubric set by industry experts.
Since 2014, NCTQ has encouraged TPPs to increase the number of course hours in mathematics. As such, the rubric relies heavily on recommended graded instructional hours for each of five topics: numbers and operation (45 hours), algebraic thinking (20 hours), geometry and measurement (25 hours), data analysis and probability (15 hours), and pedagogy (45 hours), for a total of 150 instructional hours.
While undergraduate programs increased their total credit hours over the past decade, not all programs allocate hours with the recommended balance across all five topics that NCTQ considers essential. As a result, just 14% of undergraduate programs earned an A, while 20% scored an F. This distribution of grades reflects a shortfall in average content hours and an excess in pedagogic hours relative to what is recommended. “Numbers and operation” and “algebraic thinking” have the largest gap in content hours.
On average, public institutions offer a similar number of pedagogical hours to private institutions, but significantly more content hours. And while undergraduate program evaluations are a mixed bag, that is not the case for graduate programs; 83% earned an F. Graduate institutions averaged 14 content hours, compared to a recommended minimum of 105. NCTQ does not explain why so few content hours are required. For example, students in graduate programs may have the necessary math content courses in their undergraduate studies or possess completion of a state’s basic skills test in math. Because of this, our focus is on undergraduate programs.
The report highlighted actions both TPPs and state policymakers can take to improve math instruction, including more time spent on content instruction, feedback loops between prep providers and schools, and more explicit standards for program approval and licensure testing. They also suggested states develop pathway programs intentionally designed to address shortages.
Why This Matters in Minnesota
Minnesota has 24 undergraduate TPPs. The report gave 11 grades of B or higher and 11 grades of C or lower (two were not determined).
|2022 NCTQ Elementary Mathematics Grade||Number of Undergraduate TPPs|
|*Cannot be determined|
Taking a closer look at hourly minimums for individual topics at the 11 schools earning a B or above, it is easy to spot shortfalls. Five TPPs are short total hours (each at 15). Only two fall short on pedagogical instruction hours. But just two schools meet or exceed the hours for algebraic thinking. For three of the eight B-graded programs, rearranging existing hours would move them into the A category. For these TPPs, meeting the NCTQ recommended hours is well within reach.
TPPs earning a C or lower offer a more challenging landscape. For example, one reported 120 hours in pedagogy and zero in content, and another 30 hours in pedagogy and zero in content. Setting those aside and focusing on the remaining eleven, the average shortfall is 59 content hours—with a one-hour average “surplus” in pedagogy.
These findings imply that Minnesota undergraduate TPPs may send many elementary teachers into the classroom without a solid grounding in math content. In recent years, policymakers, advocates, and educators have begun working to address gaps in literacy instruction and preparation. However, there is still little conversation about math and the impact this has on student outcomes. From program design and approval to structure and content—even testing where Minnesota combines mathematics, health/fitness, and fine arts into a single test—several avenues could lead to more effective TPP instruction.
Read the Full Analysis
A Meta-Analysis of the Relation Between Math Anxiety and Math Achievement
Psychological Bulletin, 2021
Scientific knowledge tends to move incrementally. And that is the case for understanding the relationship between factors that underlie attitudes about math and math achievements. In her 1960 publication, Rosalind L. Feierabend utilized about one-third of her article (excluding her extensive bibliography of more than 280 entries) to grapple with “factors underlying attitudes” toward mathematics. She asked three questions for further research:
- Is there a prevailing negative attitude toward arithmetic and mathematics?
- What is the relationship between motivation and achievement?
- What are the factors underlying attitudes toward mathematics?
This study adds to several decades of scholarship on this question.
The authors look at the relationship between math anxiety and math achievement, investigating research from 1992 to 2018. They explore how the relationship varies based on gender, race/ethnicity, grade level, how math anxiety is measured, and the specific content area. Overall, the results show a small to moderate correlation between math anxiety and achievement.
Students with “low math ability” were more likely to have math anxiety. In addition, there were statistical differences between grade groups. For example, grades 1-2 and 3-5 had lower math anxiety compared to grades 9-12, and grades 6-8 and 9-12 had higher math anxiety than postsecondary students. One additional finding is worth noting: The prevalence of math anxiety increases when the content assessed utilizes a standardized test (e.g., ACT, MCA, or NAEP) compared to anxiety associated with taking a unit test given by a teacher.
The authors did not find statistically significant differences across lines of gender, nationality, race/ethnicity, or among adults, teachers vs. non-teachers.
Why This Matters in Minnesota
Math is a language and inherently cumulative. For example, addition, subtraction, multiplication, and division build on the knowledge of real numbers; fractions require an understanding of division, and so on. Therefore, building a command over the grade-level math content is critical, especially at the early elementary levels. When this does not happen, math anxiety may appear or heighten.
Reducing student math anxiety is complicated and symbiotic with teaching; a student’s level of anxiety may be heightened when the teacher is not sufficiently confident in their own instruction.
Math competency is critical for college and career readiness—and many Minnesota students are falling behind where they should be able to succeed, in fields from STEM to financial services, even education. Data indicate that Minnesota does relatively well compared to national averages. However, with fewer than half of all 8th-graders scoring proficient or advanced on the National Assessment of Educational Progress, there is little reason to celebrate. For students who are from low-income households, Black, Latino, Indigenous, or English Learners proficiency in math ranges from 4-22%. Failing to address this contributes to disparate outcomes in both college and the workforce.
Read Full Article
Not All Elementary School Teachers Are Scared of Math
Journal of Numerical Cognition, 2021
This study analyzed pre-service and current elementary teachers in Germany and Belgium and their relative comfort/anxiety with mathematics, using university students in other fields of study as a benchmark. All took an Abbreviated Math Anxiety Scale (AMAS) survey. In addition, it looked at teachers specializing in math and in other fields, allowing for an additional layer of comparison.
The study found a high number of teachers not specializing in math experienced “critical math anxiety”—estimated to be as high as 23% of teachers. In fact, this group experienced higher rates of math anxiety than university students overall. Findings were significantly different for teachers who chose to specialize in math. For that subset, only 5% experience critical math anxiety. Not surprisingly, they also experience greater enjoyment and ease in teaching math. Another notable finding is that, while specializing in math correlates with lower levels of math anxiety, experience teaching math does not—indicating that it needs to be addressed independently.
There are a few limitations to keep in mind. First, because of overall teacher workforce demographics analysis was limited to female teachers. Second, while we can see clear correlations, we do not know what may be causing them. Finally, we do not know if the findings are generalizable to other countries and/or education systems.
Why This Matters in Minnesota
While this study was conducted abroad, there is good reason to think it could also have implications for Minnesota. In terms of math proficiency as a nation, we lag behind those in the study. The PISA 2018 Math rankings—a standardized international measure of achievement—place Belgium at 15th, Germany at 20th, and the United States at 37th. In the U.S., the National Assessment of Educational Progress ranks Minnesota significantly above the national average on math achievement overall—but with a proficiency rate of 44%, there is little cause for celebration.
A big takeaway: Elementary school teachers without a specialization in math have higher levels of math anxiety and lower levels of enjoyment when teaching math. These outcomes appear not to diminish with teaching experience. However, pre-service and current teachers with a specialization in math do not have higher levels of math anxiety and, instead, experience higher levels of enjoyment when teaching math. We should therefore consider how we address both math proficiency and anxiety for prospective and current teachers who may teach the topic but did not choose to specialize in it. This can begin by ensuring elementary-school teacher preparation programs include adequate math content instruction as the National Council on Teacher Quality recommends.
Read the Full Study