Mathematics teachers face many critical issues related to instruction, including those connected to student motivation, conceptual understanding, technology use, access and equity, and others. When defining critical issues in mathematics education, we borrow from Merriam Webster’s (n.d.) definitions of critical and issue to frame what is meant. According to the definitions, critical “can be of, relating to, or being a turning point or specially important juncture” and an issue is a “vital or unsettled matter,” that is, a problem or concern. Thus, critical issues in mathematics education, either individually or collectively as a field, are important areas that raise questions about a problem or concern that impacts mathematics teaching or learning. The National Council of Teachers of Mathematics (NCTM, 2014) described unproductive beliefs and issues in mathematics education, including an emphasis on teaching procedures without meaning, low expectations for students, limited access to necessary tools and technology, and high-stakes testing. Critical issues within access and equity arise in the form of tracking and gender, racial, and socioeconomic status disparities in the classroom (Aguirre et al., 2013; Buckley, 2010; NCTM, 2018, 2020). Low motivation and engagement are critical issues seen in mathematics classrooms, leading to a decline in mathematical performance and impacting the mathematics courses students take in the future (Bobis et al., 2016).

Preservice teachers (PSTs) must learn to identify and confront critical issues in teaching and learning mathematics, and mathematics teacher educators should find additional ways to support PSTs in navigating these issues. Darling-Hammond (2006) explained that PSTs should, “understand deeply a wide array of things about learning, social and cultural contexts, and teaching and be able to enact these understandings in complex classrooms serving increasingly diverse students” (p. 302). The Association of Mathematics Teacher Educators' (AMTE, 2017) Standards for Preparing Teachers of Mathematics highlighted the importance of supporting PSTs in connecting research and practice. Mathematics teacher educators must find additional ways to help prepare PSTs for the rigors of the content while supporting their understanding of how to identify and confront critical issues in mathematics education, particularly in light of relevant research.

As mathematics teacher educators who work with middle and secondary PSTs, we noticed that many PSTs were initially unaware of the challenges of critical issues related to teaching and learning mathematics and navigating them with agency. It became necessary for us to find an additional way to connect the experiences of our PSTs in their clinical practice to the content of a course called Critical Issues in Mathematics Education. The approach we took used NCTM’s (2014) Mathematics Teaching Practices and Essential Elements as a way to organize questions around critical issues in teaching and learning mathematics. To support PSTs in addressing these critical issues in authentic ways, we developed a Vignette Activity Sequence (VAS) to provide PSTs with opportunities for focused reflections using a recording sheet. In the following sections, we share information about the critical issues course and explain how we use the VAS to help PSTs identify and confront critical issues in teaching mathematics as part of their coursework.

Description of the Course

All middle grades and secondary PSTs majoring in mathematics education in our program complete a course called Critical Issues in Mathematics Education. In this course, PSTs generate questions that inform the schedule and topics for the course. During the first class meeting, PSTs identify critical issues specific to mathematics education through brainstorming and listing their experiences as mathematics learners and as mathematics PSTs. They generate questions based on what they have noticed as students of the subject and their wonderings about issues they have experienced during clinical practice. The course instructor organizes the questions around critical issues related to NCTM’s (2014) Mathematics Teaching Practices and Essential Elements, which make up the weekly topics. The course instruction and learning activities are designed to help PSTs answer the PST-generated questions, which guide class discussions each week. Table 1 shows a sample of PST-generated questions.

Table 1. Sample of PST-Generated Questions

The course includes several assignments designed to support PSTs’ understanding of these critical issues and to make connections to their clinical practice. The major project for the course requires each PST to engage in independent reading of research articles and books about their weekly topic and the related critical issues. To determine the PST’s major project topic, PSTs choose two or three weekly topics that they would like to be their project topic so that the instructor can organize the assignments and try to accommodate each PST’s preference. For this project, the PST reads existing research to write a paper on the weekly topic and related critical issues. They also create a lesson plan that includes an engaging activity to present during a portion of class that week. In the same week, a separate assignment requires another PST to read a related research article on the same weekly topic and write a summary of the article. To contribute to class discussion that week, the second PST shares what they read and poses a related question to their peers in class. In this way, two PSTs are sharing information about the weekly topic and related critical issues. The instructor also presents additional information about the weekly topic and related critical issues, including seminal studies, recently published research, and related resources. Other course assignments include the VAS assignments, PSTs writing weekly reflective journals related to the weekly topics, collecting and analyzing clinical practice data related to the weekly topics and critical issues, and a written final exam on which PSTs position themselves by responding to prompts about various critical issues.

During the same semester, PSTs are placed in a local school for a clinical experience. PSTs partner with an assigned classroom teacher for 2 class periods a day, 4 days a week, and they plan and teach several lessons during this time. Students make connections between the critical issues course and their clinical experiences by engaging in a VAS, which we describe in the following section.

Description of the Vignette Activity Sequence

One challenge for mathematics teacher educators is the fostering of PSTs’ recognition and analysis of critical issues while in clinical practice. We address this challenge in our mathematics teacher education program by using vignettes. Jeffries and Maeder (2011) defined vignettes as “a specific type of short, descriptive story that describes a problem related to course content in order to stimulate discussion” (p. 162), while asserting that vignettes allow exploration of difficult topics. Vignettes also provide an opportunity for PSTs to make connections between the published research they read in our course and what they observe in their clinical experience.

We developed the VAS to support PSTs’ understanding of Mathematical Practices (National Governors Association Center for Best Practices & the Council of Chief State School Officers, 2010), the Mathematics Teaching Practices (NCTM, 2014), and critical issues. The VAS has two phases. In Phase I, PSTs read 3-4 instructor-authored vignettes throughout the semester. While reading the vignette, they complete an accompanying recording sheet, identifying the Mathematical Practices, Mathematics Teaching Practices, and critical issues they identify in the vignette. PSTs also reflect on and document how this vignette relates to and could impact their clinical practice. For examples, see Shelton et al. (2020), Shelton et al. (2021), and Wilkerson et al. (2018).

Phase II of the VAS supports a transition from identifying critical issues to confronting critical issues in practice. In Phase II, PSTs create their own vignette and recording sheet based on an observation they make about a critical issue related to teaching and learning mathematics in their clinical practice. For example, they could write a vignette about a specific instance of technology use or access and equity. By writing their own vignette, they bring their experiences with critical issues in mathematics education back to their critical issues course for discussion. We provide a sample of a PST-created vignette in the Appendix. In the PST-created vignette, the PST recognizes an issue of access and equity in the classroom. The PST who wrote this vignette observed an equity issue regarding a student’s prior experiences in the classroom and recorded the resulting experience in a vignette. On the surface, it seemed as though the student did not understand the mathematics concept being taught. When looking deeper, the student understood the mathematics but could not access the mathematical skills to solve it because they did not understand the scenario in the given problem. This situation illustrates how powerful PST-created vignettes can be, as this vignette allowed the PST to bring something that happened in clinical practice to the critical issues course for discussion with their peers and course instructor.

Suggestions for Using the Vignette Activity Sequence

Mathematics teacher educators should consider how they can help PSTs identify and confront critical issues in mathematics education by supporting PSTs in looking for connections between the content addressed in their university courses and confronting critical issues in clinical practice (see Standards C.2 and C.4 in AMTE, 2017). Using the VAS and the related recording sheet can help PSTs identify and confront issues in mathematics education, as having PSTs create their own vignettes directly drawn from their experiences in the classroom can help bridge the connection between theory and practice. The VAS also has the potential to strengthen collaboration between PSTs and their assigned classroom teachers in whose classrooms they teach. To prepare for the critical issues that PSTs may experience, at the beginning of the year PSTs and teachers could brainstorm their own questions related to critical issues in mathematics teaching and learning. As PSTs work with their assigned classroom teacher, they can spend time identifying and confronting critical issues impacting their classroom.

Teachers in other disciplines could also generate essential questions representing critical issues they observe in the classroom. Bringing their questions and observations to their colleagues to discuss them and develop action plans in a structured format could be one form of professional development, similar to the way we used the VAS in Shelton et al. (2020). They can also draw connections to professional standards, school initiatives, or research.

Appendix: PST-Created Vignette

In class, the students are working on writing linear equations in the form y=mx+b. Students are given a worksheet with a variety of situations on it and are expected to write equations based on the situation given. One such situation is as follows: Juan goes to the bowling alley. He must pay $5 for his shoes, and then $3.50 per game. Write a linear equation representing the situation. 

One student has asked for help with this problem. She has copied down the problem but has not made any progress in solving it. The discussion between the student and Ms. Jones is as follows:

Student:        I do not get this problem.

Ms. Jones:    Okay, well where do you think you should start?

Student:        I need to find which number goes with the x, but I do not know which one to choose.

Ms. Jones:    So, when we have the equation like y=mx+b, which thing only happens once? The number with the x, or the other number.

Student:        The other number.

Ms. Jones:    Right! So, the m, or the number with the x, is the slope, and the other number, b, is the y-intercept. So which of these things in the problem only happen once- the paying for shoes or the paying for games?

Student:        What do you mean?

Ms. Jones:    When you go bowling, how many times do you pay for the shoes?

Student:        I do not know; I have never been bowling before.

Ms. Jones then explains to the student that when you go bowling you pay once for your shoes, and then you pay per game. The student recognizes that the price for the shoes is then the y-intercept because they would pay that price once, even if they played no games, and the price per game is the slope because that price depends on how many games you play. The student writes the equation: y=3.5x+5.

References

Aguirre, J., Mayfield-Ingram, K., & Martin, D. (2013). The impact of identity in K–8 mathematics learning and teaching: Rethinking equity-based practices. National Council of Teachers of Mathematics.

Association of Mathematics Teacher Educators. (2017). Standards for Preparing Teachers of Mathematics. Retrieved from www.amte.net/standards

Bobis, J., Way, J., Anderson, J., & Martin, A. J. (2016). Challenging teacher beliefs about student engagement in mathematics. Journal of Mathematics Teacher Education, 19(1), 33–55.

Buckley, L. A. (2010). Unfulfilled hopes in education for equity: Redesigning the mathematics curriculum in a US high school. Journal of Curriculum Studies, 42(1), 51–78.

Darling-Hammond, L. (2006). Constructing 21st-century teacher education. Journal of Teacher Education, 57(3), 300–314. doi:10.1177/0022487105285962

Jeffries, C., & Maeder, D. W. (2011). Comparing vignette instruction and assessment tasks to classroom observations and reflections. The Teacher Educator, 46(2), 161–175. doi:10.1080/08878730.2011.552667

Merriam-Webster. (n.d.). Merriam-Webster.com dictionary. Retrieved April 6, 2023, from www.merriam-webster.com/dictionary/

National Governors Association Center for Best Practices & the Council of Chief State School Officers. (2010). Common core state standards for mathematics. Retrieved from https://ccsso.org/resource-library/common-core-state-standards-mathematics

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Author.

National Council of Teachers of Mathematics. (2018). Catalyzing change in high school mathematics: Initiating critical conversations. Author.

National Council of Teachers of Mathematics. (2020). Catalyzing change in middle school mathematics: Initiating critical conversations. Author.

Shelton, R. N., Kerschen, K., & Wilkerson, T. L. (2020). Investigating teachers’ understanding of mathematical practices and mathematics teaching practices using a vignette activity sequence in a professional development setting. School-University Partnerships, 13(2), 38–46.

Shelton, R. N., Kerschen, K., & Wilkerson, T. L. (2021). The examination of a vignette activity sequence in a secondary mathematics methods course. School Science and Mathematics, 121(1), 2–12. doi:10.1111/SSM.12445

Wilkerson, T. L., Kerschen, K., & Shelton, R. N. (2018). Preservice teachers’ critical connections to effective mathematical teaching practices: An instructional approach using vignettes. Action in Teacher Education, 40(4), 358–373. doi:10.1080/01626620.2018.1512430