The purpose of this study is to explore the strengths and weaknesses of the mathematical knowledge of U.S. preservice middle school mathematics teachers from the Mathematics Teaching in the 21st Century (MT21) study (Schmidt, et al., 2007). My intention is to shed light on the means reported in the study for U.S. preservice teachers. What specific skills do preservice middle school teachers lack? What does this imply for middle school teacher education?

Perspectives

The MT21 Study

            The goal of the MT21 study was to find out how middle school teachers were prepared in a small number of countries. The researchers wanted to know how certain variables in the areas of achievement, opportunity to learn, and beliefs varied across countries.

            The U.S. sample for the MT21 study came from 12 universities across the nation. (I have data from two of those universities and I will obtain more soon.) The sampled preservice teachers were in their last year of their program.

DCMs

            In order to isolate the specific skills in number sense, algebra, and geometry that the U.S. preservice teachers have mastered and have not mastered, I used diagnostic classification models (DCMs; Rupp, Templin, & Henson, 2010). In essence, DCMs can take the responses given by a participant in a survey or test and categorize that participant in his or her place as a master of one of any possible combinations of skills tested.

Methods

Item Analysis

            I located the items testing number, algebra, and geometry skills. For number sense, I chose items whose skills required the preservice teachers to categorize sets of numbers as natural numbers, integers, rationals, reals, or complex numbers (5 skills). For algebra, I chose items whose skills required the preservice teachers to add, subtract, multiply, divide, and/or take the square root of both sides of an equation (5 skills). For geometry, I chose items whose skills required the preservice teachers to use the definition of a point, the definition of a segment, the definition of an equilateral triangle, the circle property in which two inscribed angles that intercept the same arc are congruent, and another circle property in which the angle measure of an inscribed angle is half the angle measure of a central angle if they intercept the same arc (5 skills).

DCM Analysis

            I followed the recommendations for DCM analysis set forth in Rupp, et al. (2010). The statistical program Mplus (Muthen & Muthen, 1998-2011) was used to classify all participants into their respective classes.

Data Sources

I have collected data from 42 participants from two U.S. universities that participated in the MT21 study. (Soon, I plan to obtain and analyze data on about 200 more participants from the other 10 universities that were sampled.)

Preliminary Results

Number Sense Skills

            There were 21% of preservice teachers that could not be considered as masters of classifying sets of numbers (see Figure 1a). Here is an area in which the preservice teachers could likely use more experience and study in their preparation programs.  (I am still working on possible recommendations to make for teacher preparation programs.) On the other hand, there were 5% that could classify all number sets correctly.

Algebra Skills

            The results for preservice teachers' ability to perform single algebraic manipulations are found in Figure 1b. There were 38% of the preservice teachers that were not masters of any algebraic skill. Additionally, there were no participants that were considered masters of these skills.  Certainly, work is needed here to help preservice teachers understand and perform these basic algebraic skills.

Geometry Skills

            The results for preservice teachers' abilities in geometry are presented in Figure 1c. Here, 33% of the preservice teachers were masters of all concepts.  However, 31% were also not masters of any concept.  Again, because there are a good number of preservice teachers that are not masters of all the geometric concepts I analyzed, geometry can be another area for preservice teachers to review.

Figure 1a. U.S. Middle School Preservice Teachers' Knowledge of Select Numerical Concepts. N = master of accurately classifying given set of numbers to the set of natural numbers (simplified as "set of natural numbers"); Z = "set of integer numbers;" Q = "set of rational numbers;" R = "set of real numbers;" C = "set of complex numbers."

Figure 1b. U.S. Middle School Preservice Teachers' Knowledge of Select Algebraic Concepts.
+ = successfully adding equal amounts to both sides of an equation (simplified as "add both sides"); – = "subtract both sides;" x = "multiply both sides;" / = "divide both sides;" \/ = "square root both sides."

Figure 1c. U.S. Middle School Preservice Teachers' Knowledge of Select Geometric Concepts.
. = successful use of the definition of a point in a proof (simplified as "definition of a point"); – = "definition of a segment;" /_\ = "definition of an equilateral triangle;" 2iLs = "property of two inscribed angles that intercept the same arc are congruent;" iL-cL = "property of the angle measure of an inscribed angle is half the angle measure of a central angle if they intercept the same arc."

Educational Importance

There has been a call made by the National Academy of Education (NAEd) to improve the quality of our K-12 teachers in the U.S. to meet the needs of all students. They began their white paper by stating:

Improving teacher quality thus entails policies concerning recruitment, early preparation, retention (including attention to working conditions), as well as professional development (Wilson, 2009, p. 1, emphasis added).

The NAEd further suggested that research into improving such programs should investigate structure, curriculum, enrollment, and the opportunities they provide to develop the skills they need for practice (Wilson, 2009). The challenge here is to identify the knowledge and skills that are both necessary for new teachers and within their reach.

Assessment Systems

            This project is also investigating the system of assessing teachers' mathematical knowledge.  I will discuss the validity of assessing and whether or not they were able to measure what they wanted to measure based on the results for the U.S.

References

Muthen, L. K., & Muthen, B. O. (1998-2011). Mplus Version 5.1 [Computer software]. Los Angeles, CA: Authors.

Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic measurement: Theory, methods, and applications. New York: The Guilford Press.

Schmidt, W., Tatto, M. T., Bankov, K., Blšmeke, S., Cedillo, T., Cogan, L. et al. (2007). The preparation gap: teacher education for middle school mathematics in six countries. East Lansing, MI: Michigan State University.

Wilson, S. (Ed.). (2009). Teacher quality education policy white paper. Washington, DC: National Academy of Education.