Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.
Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh
Joshua T. Hertel and Tami S. Martin
The November 2013 issue of JRME marks the end to the 44th volume. Looking back on the history of the journal, many things have changed since the first issue was published in January 1970. In particular, the process through which manuscripts are submitted, reviewed, and published has changed greatly. Gone are the days of mailed manuscripts and reviews. As the journal has matured with the field of mathematics education, the standards and expectations for both manuscripts and reviews have also evolved. These standards and expectations are to a great extent influenced by the peer-review process and are thereby linked to the practice of blinding. When submitting a manuscript to JRME, authors must submit both a blinded and an unblinded version. The blinded version is sent to reviewers, and the unblinded version is used by the editorial staff. Although other journals use a single-blind process (reviewers are aware of the identities of the authors) or an open review process (both parties are aware of the others' identities), the JRME review process remains a double-blind process in which neither authors nor reviewers are aware of the others' identities.
Nicholas J. Gilbertson, Samuel Otten, Lorraine M. Males, and D. Lee Clark
For many American students, high school geometry provides their only focused experience in writing proofs (Herbst 2002), and proof is often viewed as the application of recently learned theorems rather than a means of establishing and understanding the truth of general results (Soucy McCrone and Martin 2009).
This department publishes brief news articles, announcements and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education. This month in the Coaches' Corner, take a closer look at CCSS Standard 3 for Mathematical Practice, Explain and Justify. Coaches may want to demonstrate the integration of math and writing with Speak, Write, Reflect, Revise, a five-step approach for integrating problem solving and the writing process.
James E. Tarr, Douglas A. Grouws, Óscar Chávez, and Victor M. Soria
We examined curricular effectiveness in high schools that offered parallel paths in which students were free to study mathematics using 1 of 2 content organizational structures, an integrated approach or a (traditional) subject-specific approach. The study involved 3,258 high school students, enrolled in either Course 2 or Geometry, in 11 schools in 5 geographically dispersed states. We constructed 3-level hierarchical linear models of scores on 3 end-of-year outcome measures: a test of common objectives, an assessment of problem solving and reasoning, and a standardized achievement test. Students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the standardized achievement test. Significant student-level predictors included prior achievement, gender, and ethnicity. At the teacher level, in addition to Curriculum Type, the Opportunity to Learn and Classroom Learning Environment factors demonstrated significant power in predicting student scores, whereas Implementation Fidelity, Teacher Experience, and Professional Development were not significant predictors.
Douglas A. Grouws, James E. Tarr, Óscar Chávez, Ruthmae Sears, Victor M. Soria, and Rukiye D. Taylan
This study examined the effect of 2 types of mathematics content organization on high school students' mathematics learning while taking account of curriculum implementation and student prior achievement. The study involved 2,161 students in 10 schools in 5 states. Within each school, approximately 1/2 of the students studied from an integrated curriculum (Course 1) and 1/2 studied from a subject-specific curriculum (Algebra 1). Hierarchical linear modeling with 3 levels showed that students who studied from the integrated curriculum were significantly advantaged over students who studied from a subject-specific curriculum on 3 end-of-year outcome measures: Test of Common Objectives, Problem Solving and Reasoning Test, and a standardized achievement test. Opportunity to learn and teaching experience were significant moderating factors.
David W. Stinson
This article shows how equity research in mathematics education can be decentered by reporting the “voices” of mathematically successful African American male students as they recount their experiences with school mathematics, illustrating, in essence, how they negotiated the White male math myth. Using post-structural theory, the concepts discourse, person/identity, and power/agency are reinscribed or redefined. The article also shows that using a post-structural reinscription of these concepts, a more complex analysis of the multiplicitous and fragmented robust mathematics identities of African American male students is possible—an analysis that refutes simple explanations of effort. The article concludes, not with “answers,” but with questions to facilitate dialogue among those who are interested in the mathematics achievement and persistence of African American male students—and equity and justice in the mathematics classroom for all students.
Na'ilah Suad Nasir and Maxine McKinney de Royston
This article explores how issues of power and identity play out in mathematical practices and offers a perspective on how we might better understand the sociopolitical nature of teaching and learning mathematics. We present data from studies of mathematics teaching and learning in out-of-school settings, offering a sociocultural, then a sociopolitical analysis (attending to race, identity, and power), noting the value of the latter. In doing so, we develop a set of theoretical tools that move us from the sociocultural to the sociopolitical in studies of mathematics teaching and learning.
Indigo Esmonde and Jennifer M. Langer-Osuna
In this article, mathematics classrooms are conceptualized as heterogeneous spaces in which multiple figured worlds come into contact. The study explores how a group of high school students drew upon several figured worlds as they navigated mathematical discussions. Results highlight 3 major points. First, the students drew on 2 primary figured worlds: a mathematics learning figured world and a figured world of friendship and romance. Both of these figured worlds were racialized and gendered, and were actively constructed and contested by the students. Second, these figured worlds offered resources for 1 African American student, Dawn, to position herself powerfully within classroom hierarchies. Third, these acts of positioning allowed Dawn to engage in mathematical practices such as conjecturing, clarifying ideas, and providing evidence.
Jennifer Noll and J. Michael Shaughnessy
Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.