Middle school mathematics classroom practices and achievement: a TIMSS-R analysis

Focus on Learning Problems in Mathematics, Fall, 2004 by James A. Telese

Steffe and D'Ambrosio (1995) argue for reflection from a constructivist perspective. It is through reflection that one critiques and/or compares and contrasts one's own thoughts with those of others in a dialogic format. In order to encourage reflection, there are three prevailing actions that mathematics teachers can use to assist in the development of a learning space as discussed above: (1) pose situations that students regard as genuine problems, (2) model reflective actions, and (3) facilitate interactive, mathematical communication to activate schemes such as prior knowledge. It is thought that activating prior knowledge leads to generalizing assimilation (or, transfer of learning). This implies that social interaction, "underlies all teaching actions" (p. 156). In this regard, verbal and nonverbal communication becomes a major component of a constructivist environment.

Method

Sample

The TIMSS sample design was a two-stage cluster design where schools were selected in the first stage followed by classrooms in the second stage. Various types of information were collected as part of the TIMSS-R student questionnaire, including student characteristics, instructional activities, family characteristics, out-of-school activities, learning resources, and achievement. Students included in this analysis were from the TIMSS Population 2 International Sample (13 year-olds) from the United States. The reader is reminded that the survey was administered to students who self-reported their perception of the frequency that the selected activities occurred in their classrooms. As with any survey data, the data may be questioned as to whether the respondents are responding truthfully to the statements.

Measures

The TIMSS-R measures achievement in five mathematics categories and provides an overall mathematics achievement score. The five reporting categories were: (1) Fractions and Number Sense, (2) Measurement, (3) Data Representation, Analysis and Probability, (4) Geometry, and (5) Algebra. There was a variety of item types that included, multiple-choice, short answer, and extended response, with a total of 162 items, but students do not respond of all of the items (Gonzalez & Miles, 2001a). Items have been released to the public, which may be accessed at the following website: http://isc.bc.edu.

Six variables were chosen from the instructional activities section of the TIMSS-R student survey in response to the question, "How often does this happen in your mathematics lesson?" The six selected variables were the following: (1) "We work on mathematics projects," (2) "We use calculators," (3) "We work together in pairs or small groups," (4) "We discuss our completed homework," (5) "Students use the board," and (6) "Students use the overhead projector." The author presumes that students would be required to explain their thinking while at the board or the overhead; the survey does not make this clear. Two other variables from the survey were selected in response to the question: "When we begin a new topic in mathematics we begin by ...?" (1) "Discussing a practical or story related to everyday life, and (2) "Having the teacher ask us what we know related to the new topic." On each of these instructional activities, students indicated the frequency using a Likert-scale where a one indicated "almost always," a two, "pretty often," a three, "once in a while," and a four, "never." The dependent measures for this study were the TIMSS-R Overall Mathematics score, and the content area scores for Algebra, Data and Probability, Fractions/Number Sense, Geometry, and Measurement.