The implementation of higher mathematics standards across the nation understandably creates a need for substantial support for teachers. Ensuring that every student succeeds in math is a daunting task. Teachers understand that there is no room for poor-quality teaching in any math classroom—the stakes are too high. However, being an excellent teacher every day, multiple times a day, requires a significant amount of knowledge, expertise, and effort. Thankfully, the community of math educators has made considerable progress with support and guidance from local and national organizations such as the National Council of Teachers of Mathematics (NCTM).
Despite these efforts, understanding why there are so many students underperforming in mathematics across the nation is not so simple (Hussar et al., 2020). Numerous complex factors contribute to student performance; among them, four are notable in the literature: (1) students’ attitudes towards math, (2) teachers’ low expectations about what students can achieve, (3) teachers’ content knowledge and understanding of how to deliver the content effectively and (4) the challenges of implementing quality curriculum materials (Hattie et al., 2016, 38-47).
Regarding the first factor, it is evident that students’ perception of their ability to succeed in mathematics is of significant importance to their achievement. Beliefs and attitudes towards the discipline are of great consequence (Gonzalez & Maxwell, 2018), and themselves depend on what teachers expect of their students. Teachers’ beliefs, attitudes and expectations about their students have a great impact on students’ attitude towards the subject -mathematics (Saenz et al., 2023, 304-322). While students might not always effectively communicate their emotions and feelings to others, they have a strong sense of how their teachers feel about them. They know when their teachers like them or not; they know when teachers expect the best of them. Simply put, teachers’ beliefs about their students matter —students can perceive and feel it (Mason, 2010, 73-85). Which brings us to the second factor, low expectations about what students can do.
Such expectations take a lack of student motivation in mathematics as a given, and diminished achievement as a consequence. So, it is worth asking: what teacher qualities have the most influence on their students’ beliefs and attitudes towards mathematics? Researchers have identified at least two key qualities: the teacher’s passion for, and deep knowledge of, the discipline, combined with their expertise in teaching it (Saenz et al., 2023, 305-6; Gonzalez & Maxwell, 2018, 8). It is almost as if the teacher’s love and admiration for the subject were contagious. Students cannot help but be immersed in the teacher’s enthusiasm and genuine appreciation for mathematics as a way of thinking, and understanding the world. Modeling the power of mathematics and its endless fascination, teachers are naturally motivated to share its beauty with their students.
This enthusiasm is closely related to the third factor, the teacher’s knowledge. Yet, how do teachers cultivate their knowledge and passion for mathematics? First, it is worth noting that math teachers are not a monolithic group. Although typically, math teachers are a self-selected group of people with a good disposition towards mathematics, their attitudes, expertise, and experiences fall along a continuum of knowledge. In my experience, math educators share a deep desire to grow intellectually and learn more about the mathematics they teach, and how to better support their students’ learning trajectories.
To achieve this, math educators welcome professional learning (PL) activities designed to improve their knowledge and skills. However, not all PL activities are created equal, and math educators are known for having a notoriously low tolerance for PL activities that they perceive as a waste of time. Effective PL is rooted in a community of learners, focused on deepening content knowledge alongside research-based teaching practices, and it happens continuously over time, generally six months or more (National Council of Teachers of Mathematics, 2014, 99-108).
Throughout my career, I have observed math educators cultivate their knowledge and passion for mathematics by engaging in professional learning communities that allow them to belong to a community of professionals. It is in such environments that math identities are nurtured, and their sense of responsibility as the ‘owners’ of mathematics are developed. This sense results in mutual accountability: to each other, to the students, and to their communities. As their identity as ‘mathematicians’ develops, so does their ownership of the state of mathematics in their communities.
It follows as an inescapable conclusion, that engaging teachers in meaningful professional learning communities (PLCs) can have a positive impact on teachers’ knowledge and behavior, therefore such communities matter. They matter because they can have an indirect impact on student achievement by improving the skills of their teachers. This is a claim that has been consistently backed by research (Opper, 2019; Polly et al., 2017; Rivkin et al., 2005; Xu & Swanlund, 2013; Yoon et al., 2007)
Although it is clear that PLCs matter, and the need for professional learning activities is perennial, the fact remains that there is a shortage of high-quality opportunities. This is in part because to be effective, a professional learning activity should not only be centered around a community, but also be: cohesive, of sufficient duration, engaged in active learning, focused on content knowledge and be tied to quality curriculum materials (Yoon et al., 2007). This last criterion presents its own challenges, which brings us to our fourth factor, implementation of quality curricular materials.
I have been fortunate to be in a position to support various curricular implementations throughout my career, and in my experience it takes time and engaged PLCs to be successful. Unfortunately, districts and schools too often give in to political pressure for immediate results, opting to change curricular materials before they are given a chance to succeed. It is difficult for a single curriculum to meet the needs of all students, creating tension between fidelity to the design of the curriculum and the sometimes-necessary adaptations. Striking this balance is an overwhelming task for teachers and they often need support in the form of a PLC.
In summary:
Think about the complexity involved in supporting students who are grappling with mathematical concepts. Learning is the most difficult thing which the human brain can do. We remember our own journeys as learners, and think of the many misconceptions that naturally arise during the learning process. Recall when learning mathematics required us to transition from concrete to more abstract ways of thinking. Math requires us to see patterns, to notice quantities and the relationships between them, and which are often embedded in some contextual reality. Thinking mathematically requires us to see the real world not only through a contextual lens but also through an abstracted space where mathematics operates freely, before being subjected to the specific context in which it is ultimately applied. Math teachers are in the best position to support such a complex student learning process. But who supports them, If not a community of peers with a deep understanding of the content, and powerful insight into how we learn?
References
Gonzalez, K., & Maxwell, G. (2018, October 1). Mathematics teachers’ efficacy, experience, certification and their impact on student achievement. Journal of Instructional Pedagogies, 21(1), 1-11. https://eric.ed.gov/?id=EJ1194245
Hattie, J., Fisher, D., Frey, N., Gojak, L. M., Moore, S. D., & Mellman, W. (2016). Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning. SAGE Publications.
Hussar, B., Zhang, J., Hein, S., Wang, K., Roberts, A., Cui, J., & Smith, M. (2020, May 1). The Condition of Education 2020. The Condition of Education 2020. https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2020144
Mason, L. (2010, July 2). High School Students’ Beliefs About Maths, Mathematical Problem Solving, and Their Achievement in Maths: A cross-sectional study. Educational Psychology, 23(1), 73-85. https://doi.org/10.1080/01443410303216
National Council of Teachers of Mathematics (Ed.). (2014). Principles to Actions: Ensuring Mathematical Success for All. NCTM, National Council of Teachers of Mathematics.
Opper, I. M. (2019, December 4). Teachers Matter: Understanding Teachers’ Impact on Student Achievement. RAND. Retrieved July 16, 2024, from https://www.rand.org/pubs/research_reports/RR4312.html
Polly, D., Wang, C., Martin, C., & Lambert, R. (2017, 3). The Influence of Mathematics Professional Development, School-Level, and Teacher-Level Variables on Primary Students’ Mathematics Achievement. School Science and Mathematics, 117, 127-136. 10.1111/ssm.12214
Rivkin, S. G., Hanushek, E. A., & Kain, J. F. (2005, June 1). Teachers, Schools, and Academic Achievement. National Bureau of Economic Research, 73(2), 417-458. 10.3386/w6691
Saenz, M., Nandakumar, V., & Adamuti-Trache, M. (2023, April 18). A Comparative Study of High School Students’ Math Achievement and Attitudes: Do Math Teacher Qualifications Matter? International Journal of Education in Mathematics, Science and Technology, 11(2), 304-322. https://doi.org/10.46328/ijemst.2528
Xu, Z., & Swanlund, A. (2013, August). Estimating Teacher Contributions to Student Learning: The Role of the School Component. American Institute for Research. https://www.air.org/sites/default/files/Estimating-Teacher-Contributions-to-Student-Learning-Aug-2013.pdf
Yoon, K. S., Duncan, T., Wen-Yu Lee, S., Scarloss, B., & Shapley, K. L. (2007, October). Reviewing the evidence on how teacher professional development affects student achievement. Institute of Education Sciences. http://ies.ed.gov/ncee/edlabs