NCTM’s recent publications concerning reasoning and sense making (2009a, 2009b, 2010a, 2010b, 2011) push for high school students to be make sense of deep mathematical content to improve overall mathematical literacy. Reasoning is defined as the drawing of conclusions based on evidence where Sense Making is forming understanding of a situation, context, or concept by relating it to previous knowledge (NCTM, 2009). Reasoning is not to be seen as a list of topics but rather an approach to learning mathematics. Reasoning and sense making (NCTM, 2009) form the foundations for the processes of mathematics such as communication (NCTM, 2000).

One medium for enabling students to reason and make sense is math journals (Koirala, 2002; Marino & Angotti, 2011; Miller, 1992; Pugalee, 2001; Windsor, 2007). Journaling in mathematics has been found to help students demonstrate their mathematical understanding as well as be used as a form of assessment by teachers (Koirala, 2002). Teachers benefit from student journaling by reading student thinking in writing, a source usually not readily available to them, and by engaging with students through written feedback (Miller, 1992). Pugalee (2001) found writing to be a necessary step in the metacognitive development of students during problem solving. With journaling proven as a beneficial mechanism for mathematical understanding (Fried & Amit, 2003; Williams & Wynne, 2000), this study sought to further deepen the missing research literature on how students respond to teacher feedback in journals and how student journal writing influences classroom discourse.

Methods, Techniques, or Modes of Inquiry for the Research

The research was guided by two research questions:

(1)          How do students respond to journal feedback offered by classmates and the teacher?

(2)          How does student journal writing influence classroom discourse?

With the reasoning and sense making theoretical framework as a guide, the researcher used a grounded theory approach (Charmaz, 2006; Glaser & Strauss, 1967) to analyze data collected across two high school algebra classrooms over one semester.

Data Sources or Evidence for the Research

The instructor, who is also the researcher and university professor, co-taught an algebra class with a classroom teacher once a week for a semester as part of the instructors’ renewal of her National Board certification (NBPTS, 2011). Both classes totaled 58 students. Three data sources informed the two research questions. First, 58 students completed weekly journal entries resulting in 348 journal entries. The instructor and classmates commented on student journal entries and asked written questions in return to which students were directed to respond. Each series of journal entries was analyzed for codes and common themes (Charmaz, 2006). Second, each classroom lesson was video recorded and reviewed for codes and common themes (Charmaz, 2006). Finally, the instructor kept a weekly research log reflecting on classroom interactions including discourse surrounding journal writing (Creswell & Miller, 2000). Each iteration of data analysis invoked the constant comparative method and data was sifted into general categories (Glaser & Strauss, 1967). These categories were then compared across all documents to finalize overarching themes (Bogdan & Biklen, 1998). The three data sources allowed for triangulation of data (Merriam, 1998). Once these overarching themes were finalized, they were analyzed once more with the reasoning and sense making theoretical framework as a guide (NCTM, 2009a). 

 Results and/or Conclusions

Initials findings showed that as time progressed, student journal writings grew in length and depth (Windsor, 2007). Teacher and classmate feedback and questions to each initial journal entry forced students to reason more mathematically as they had to cite evidence to support previous conclusions they had drawn without citing the reason or evidence (NCTM, 2009a). Not all students responded to teacher and classmate feedback which suggests the need for not only modeling of initial journal entries, but also a need for a model to show how to construct responses to inquiries about their initial written responses.

A second finding showed that after students were given time to write in their journals or read responses to their journal entries, their mathematical communication (NCTM, 2000) in class was more specific and they elaborated more on their answers than during times when journal prompts were not recently discussed. The overall journal sequence, which students kept in a spiral notebook so they could refer to past entries, allowed students to make sense of how the current topic fit into previous topics we had discussed by referring back to relevant past entries (NCTM, 2009a). The teacher or the student would make references to previous class topics or journal prompts when discussing a current content topic. For example, when students were asked to explain the difference between two linear equations: the slope-intercept form and the standard form, students were able to flip back in their journals to a previous journal prompt concerning only the slope-intercept form.

Educational or Scientific Importance of the Research

Although process standards (NCTM, 2000) have been a part of mathematics classrooms in the past, NCTM’s recent push to articulate and advocate for a reasoning and sense making approach in the teaching and learning of mathematics (NCTM, 2009a) calls for researchers to pay careful attention to its implementation. This research looks at journal writing in mathematics classrooms as an avenue to strengthen reasoning and sense making. The findings demonstrate that dialogue, both written dialogue in the form of a conversation between students, classmates, and the teacher as well as verbal dialogue in the form of discussions in the classroom were enhanced by journals, however, more research is needed to determine ways to further utilize journal entries for students and teachers without it being too overwhelming for both parties (Koirala, 2002; Marino & Angotti, 2011; Williams & Wynne, 2000).

Priority Area: Assessment Systems

This poster will address the priority area of assessment systems as math journals are a form of assessment of student learning. The research analyzes student work as well as student discourse, both forms of assessment.

References

Bogdan, R. C., & Biklen, S. K. (1998). Qualitative research for education (3rd ed.). Boston: Allyn and Bacon.

Creswell, J. W. & Miller, D. (2000). Determining validity in qualitative inquiry. Theory into Practice, 39(3), 124-130.

Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. Thousand Oaks, CA: Sage Publications.

Fried, M. N. & Amit, M. (2003). Some reflections on mathematics classroom notebooks and their relationship to the public and private nature of student practices. Educational Studies in Mathematics, 53, 91-112.

Glaser, B. & Strauss, A. (1967). The discovery of grounded theory: Strategies for qualitative research. Piscataway, New Jersey: Aldine Transaction.

Koirala, H. (2002). Facilitating student learning through math journals. Proceedings of the 26^th Annual Meeting of the International Group for the Psychology of Mathematics Education: Norwich, England.

National Board for Professional Teaching Standards (NBPTS). (2011). What teachers should know and be able to do: The five core propositions of the National Board. Retrieved on July 29, 2011, from http://www.nbpts.org/the_standards/the_five_core_propositio

National Council of Teachers of Mathematics (NCTM). (2009a). Focus in high school mathematics: Reasoning and sense making. Reston, VA: Author.

National Council of Teachers of Mathematics (NCTM). (2009b). Focus in high school mathematics: Reasoning and sense making in statistics and probability. Reston, VA: Author.

National Council of Teachers of Mathematics (NCTM). (2010a). Focus in high school mathematics: Reasoning and sense making in algebra. Reston, VA: Author.

National Council of Teachers of Mathematics (NCTM). (2010b). Focus in high school mathematics: Reasoning and sense making in geometry. Reston, VA: Author.

National Council of Teachers of Mathematics (NCTM). (2011). Focus in high school mathematics: Reasoning and sense making for all students. Reston, VA: Author.

Marino, K. J. & Angotti, R. L. (2011). Mathematics journals made manageable: Using blogs and RSS feeds. Mathematics Teacher, 104(6), 466-469.

Merriam, S. B. (1998). Qualitative research and case study applications in education (Rev. ed.). San Francisco: Jossey-Bass Publishers.

Miller, L.D. (1992). Teacher benefits from using impromptu writing in algebra classes. Journal for Research in Mathematics Education, 23(4), 329-340.

Pugalee, D.K. (2001). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236-245.

Williams, N. B. & Wynne, B. D. (2000). Journal writing in the mathematics classroom: A beginner’s approach. Mathematics Teacher, 93(2), 132-135.

Windsor, M. S. (2007). Bridging the language barrier in mathematics. Mathematics Teacher, 101(5), 372-378.