Literature Review

Missing the Math

The author, Dan Meyer, explains that Common Core standards are putting a tremendous amount of pressure on teachers to produce successful students, and on parents who have becoming essentially helpless in the process. Meyer states there is equal pressure on textbook publishers to create educational materials that offer students enough relevant practice. Over the course of two years, Meyer analyzed two textbooks (86 tasks) published by McGraw-Hill, to research whether their claim of alignment with CCSSM standards was indeed validated. These two textbooks made specific claims that their tasks captured specific tasks, such as “modeling.” The author found that these textbooks fell short of their claims and recommended that teachers “Step into those gaps and provide our students with more, and more diverse, opportunities to model.” The CCSSM high school modeling standard describes five different actions that students take over the course of a complete modeling task: Identifying essential variables in a situation, formulating models from those variables, performing operations using those models, interpreting the results of those operations, and validating the conclusions of those results. This analysis suggests that textbooks offer students limited opportunities to model, and “teachers must make us for the difference.” (Meyer, 208)

Elementary Teacher Candidates’ Use of Number Strings: Creating a Math-Talk Learning Community

In this article, teacher educators focus on modeling “math-talk” for a group of teacher candidate (pre-service teachers). Common Core standards teachers to elicit student thinking, but often do know how to foster a genuine environment. Thorough lesson planning and anticipation of student responses lead to the success of this practice. The teacher educators place the pre-service in a classroom (acting as students), and model strategies ranging from teacher-led to student-led. Four major components contribute to a math-talk learning environment: questioning, explaining mathematical thinking, source of mathematical ideas, and responsibility for learning. In low-math talk classes, teachers often ask yes/no questions, and ones that simply require computation, as opposed to uncovering students’ thinking. Teachers should use “low press” questions that ask students to justify their responses (i.e. Why did you add instead of subtract?”) Teacher candidates often provide explanations because they think that what teachers do. However, students should offer their own explanation, and teachers use revoicing/retelling to repeat student answers and reinforce proper math language. Teacher candidates must also become accustomed to incorporating student ideas, and use incorrect responses to encourage student to confront their own thinking. Students can discuss each other’s responses, resulting in higher math talk. (Bofferding & Kemmerle, 2015)

Facilitating Student Interactions in Mathematics in a Cooperative Learning Setting

Leikin and Zaslavsky, conduct a case study on the benefits of cooperative learning on the basis that “communication is one of the three necessary conditions for achieving worthwhile learning objectives.” According to Vygotsky, social interaction is highly beneficial to learning, as students are more likely to be able to solve a problem in a group before working independently. Furthermore, whoel group setting tend to have a negative effect on low-achieving student. Small-group cooperative learning methods have been shown to increase learners’ participation, and interaction among classmates. At times, high-achieving students tend to “dominate” lower students. However, more often than not, low-achieving students benefit greatly from the “experts” of the group. In a study of ninth grade students, the results showed an overall increase in student interdependence, and attitudes towards learning. Lower-achieving students tended to seek the help of peers, who offered detailed explanations. The article states, “This type of help is the most powerful, according to Webb (1991), who claimed:

The content-related help that students give each other in small groups might be considered to lie on the continuum according to amount of elaboration. Detailed explanations would be at the high end of such an elaboration scale, merely stating the answer to a problem or exercise would be at the low end, and providing other kinds of information would fall in between the two extremes.” (Leiken & Zaslavsky, 1997)

All three articles hold a common theme of collaboration, high order thinking and modeling. Common Core standards are often criticized because, like the pre-service teachers in “Elementary Teacher Candidates’ Use of Number Strings,” a lot of teacher still have yet to master the art of fostering a genuine classroom filled with rich discussion, and student ideas. Teacher still rely on textbooks for modeling, but as proven in Meyer’s analysis, the textbook tends to fall short of providing students with the modeling they need to truly understand the concepts. Yes, the textbook can be used as a tool or resource. However, the responsibility still falls on the teacher to expand on that practice with enriching activities.

Bofferding, L., & Kemmerle, M. (2015, March). Elementary Teacher Candidates’ Use of Number Strings: Creating a Math-Talk Learning Community. Mathematics Teacher Educator, 3(2), 99-115.

Leiken, R., & Zaslavsky, O. (1997). Facilitating Student Interactions in Mathematics in a Cooperative Learning Setting. Journal for Research in Mathematics Education, 28(3), 331-354.

Meyer, D. (208, April). Missing the Math. Mathematics Teacher, 108(8), 578-583.