The Mathematical Education of Teachers notes “teachers need to understand the fundamental principles that underlie school mathematics, so that they can teach it to diverse groups of students as a coherent, reasoned activity and communicate an appreciation of the elegance and power of the subject.” (Conference Board of the Mathematical Sciences, 2001, p.7)
The question then arises: how do we define understanding and knowledge of mathematics? What are the courses necessary to prepare teachers of mathematics?
Universities and colleges that certify teachers neither agree on the definition of mathematical knowledge for teachers nor do they agree on the best set of courses needed to prepare teachers of mathematics. At the early grade levels some schools don’t require any mathematics courses at all. It is no wonder we read blogs like Teachers Feel Poorly Prepared In Math by JoAnne Jacobs (a reaction to Inequality for All by William H. Schmidt and Curtis C. McKnight). Many teachers claim they are not well prepared to teach mathematics at grade level or outside of the topics they currently are assigned. Jacobs relates the following in her blog, “My first husband said his sister became a second-grade teacher because she couldn’t do third-grade math. This, apparently, is not a joke.”
Unfortunately, this is not an uncommon statement heard about or by elementary teachers, and in society in general it is an acceptable thing to say. Yet, would we allow a teacher to say they taught second-grade because they couldn’t read at a third-grade level? We would immediately question how the teacher had been able to acquire a college degree and be certified to teach our children. So, how do we remedy teachers feeling and being underprepared to teach mathematics in our nation’s schools?
To date, many mathematics teacher preparation programs have required students to take standard mathematics courses geared for the general population, or alongside mathematics, engineering, and science majors. These courses tend to be taught with a “watch and do” or “sage on the stage” lecture style, giving the impression that mathematics is an established body of knowledge that many students (and society at large) feel one either “gets” or does not. Teacher candidates do not see a connection between the courses they are taking in college to the mathematics they will be teaching.
Deborah Ball and Mark Thames’ summary of Mathematics Education research in “What Math Knowledge does Teaching Require?” (TCM, Nov. 2010) finds that “conventional content knowledge”, that which is needed by mathematics-related professions such as actuaries and engineers, is not a good predictor of teachers’ effectiveness in the classroom nor is it an indicator of student achievement. This is particularly true at the K-8 level. While a teacher must have conventional content knowledge of the content they are teaching, they must also possess an expertise in understanding and evaluating how others think and learn mathematics . Courses required of future teachers must incorporate this Mathematical Knowledge for Teaching. Teachers should be required to understand the mathematics that precedes the grade level they teach as well as the mathematics that follows.
Institutes of higher education need to create standards and work together to set national guidelines. Mathematics departments need to work closely with colleges of teacher education to develop integrated coursework in order to prepare prospective teacher candidates. The Mathematical Education of Teachers II (CBMS, 2012) outlines such coursework and collaborations in detail. (See www.cbmsweb.org ) All programs preparing future teachers should follow these proposed guidelines.
In addition, teachers need to understand that it is impossible to learn everything needed to teach while they are in college. Teaching is a profession that requires life-long learning. Experiences in the classroom, self-directed study and reflection, professional development opportunities, learning communities, continuing education classes, etc. should all be a part of a teacher’s ongoing preparation throughout their career. Institutes of higher education should play a role in developing and teaching continuing education workshops and courses with a focus on teachers at various points in their careers, and school districts need to make professional learning communities a priority within their schools.
Mathematics Education research shows that in order to make mathematics curricula like those outlined in the Common Core State Standards (CCSS) and the NCTM Principles and Standards for School Mathematics, we need skilled teachers with a high level of expertise. This expertise can only be developed through strong pre-professional programs which incorporate standards set by the larger mathematics and mathematics education community and continuing education of teachers throughout their career. It is my hope that by implementing these and other standards, reports of under-preparedness in our nation’s mathematics teachers will become a distant memory and it will no longer be acceptable to society that our children’s teacher only understands second grade mathematics.
Melissa Hanzsek-Brill is a Mathematics Education faculty member of the Educational Studies/STEM Education program at Wheelock College and an Assistant Professor of Mathematics at St. Cloud State University. She earned her PhD in Mathematics Education from the University of Georgia specializing in elementary school mathematics.