Algebra student achievement has become a matter for increased focus in recent years, as educators answer calls for reform, including the standards documents of the National Council of Teachers of Mathematics and the No Child Left Behind mandates. A meta-analysis of 35 independent experimental studies shows that six teaching method categories have positive effects on student achievement in the secondary-algebra classroom. Teaching method categories are defined and ranked according to their effect sizes. Recommendations for practitioners are provided.
Student achievement in the secondary-algebra classroom has become a matter for increased focus in recent years, as educators endeavor to provide students essential skills for life in the knowledge-based economy of the 21st century (Midgett & Eddins, 2001). Ongoing reform efforts, including the standards documents of the National Council of Teachers of Mathematics (NCTM), call for robust mathematics curricula, more innovative instructional approaches, and greater access to higher-level mathematics for students traditionally steered in other directions (NCTM, 2000).
Secondary algebra is the fundamental course for students' access to higher-level mathematics. Under the auspices of the No Child Left Behind (NCLB; 2002) mandates, national and state-sponsored standardized testing programs have fostered a results-oriented instructional climate for algebra teachers and school administrators. Faced with a challenge to help all children succeed with the complexities of algebra, instructional leaders are encouraged to turn to research literature for teaching methods that enhance student achievement in secondary algebra.
There are hundreds of research reports written by educators and researchers regarding teaching methods for secondary algebra. While the literature pertaining to this topic abounds with opinion regarding curricula and anecdotal information about instructional techniques and unique classroom situations, there is a body of reports describing careful experimental studies of teaching methods in the secondary-algebra classroom. Generally, these studies each describe an experimental investigation, comparing a treatment group receiving a particular teaching method to a control group in which the method is not used. The two groups are then compared based on an outcome variable measuring the participants' algebra knowledge and skills achievement.
A formal approach to reviewing this body of research is necessary, so that educators may make data-driven decisions regarding teaching methodology. Researchers have synthesized results from education studies in order to make broad inferences. Walberg (1984) analyzed an expansive body of studies to determine three main causal influences of student learning: student aptitude, instruction, and environment. Spotlighting instruction, Marzano, Pickering, and Pollock (2001) reviewed research studies of teaching methods to specify and rank, according to effect size, nine instructional techniques that have a positive effect on student achievement across instructional situations. Each of these reviews makes a broad sweep of educational research across all grade levels, student ability levels, and settings in order to draw conclusions regarding student learning.
In an earlier and more focused study, Marcucci (1980) drew on the tenets of Glass (1976) to conduct a meta-analysis of experimental studies of teaching methods to enhance K-12 student achievement in mathematics problem solving. Marcucci reviewed 33 studies conducted from 1950 to 1980, classifying the teaching methods under investigation into four general types: modeling, systematic, heuristic, and guided discovery. Of the four teaching method types, the approach labeled heuristic-a method stressing the teaching of general problem-solving skills such as drawing diagrams or simplifying a problem by using smaller numbers-produced the strongest effects on mathematics student achievement.
Marcucci's (1980) study developed knowledge of teaching methodology for mathematics problem solving considerably. Of the 33 studies integrated by Marcucci, however, only 11 were set in an algebra classroom; thus, he was unable to draw conclusions concerning algebra instruction. Further, since 1980, new technologies and teaching methods have been introduced in the secondary-algebra classroom, allowing for a fresh appraisal of their effects (R. G. Marcucci, personal communication, September 10, 2001). Finally, Marcucci took responsibility for defining teaching method categories and assigning teaching methods to each without a content validation or classification procedure, allowing for researcher bias.
This article reports results from a meta-analysis that builds on Marcucci's (1980) methodology to review and integrate research findings from 1980 to 2002 on teaching methods for secondary-level algebra. This review of literature studies the effects of teaching methods on student achievement on Virginia's End-of-Course Test for Algebra I (Haas, 2002). It is meant to define specific teaching method types and to rank them according to their effect sizes, so that a practitioner may draw from the body of research and use its integrated findings to make pedagogical decisions. Unlike Marcucci's (1980) study, this meta-analysis includes a process for validating the assignment of individual teaching methods into teaching method categories.
Methods
Sources of Data
A representative collection of studies investigating teaching methods in the secondary-algebra classroom was gathered. The collection and selection process began by searching various computer indexes. By using three selection criteria, the initial pool of 1,418 articles was pared down to the final group of 35 studies. To be included in the meta-analysis, a study had to be conducted between 1980 and 2002 at the secondary school level (i.e., grades 7-12) where algebra instruction was the focus. Second, it had to be an experimental investigation, comparing a treatment group to a control group, whose outcome was a measure of the subject's algebra knowledge and skills achievement. Third, the teaching method in the study had to deal with algebra knowledge and skills achievement per se and not with factors related to it.
Study Characteristics
To describe the main features of the 35 studies, eight variables are presented. Two of the variables describe the types of students participating in the studies: ability level of the students as defined by the study's author as unspecified, low, middle, or high; and algebra course level as defined by the researcher as pre-algebra, algebra, or advanced algebra. The next two variables classify the treatment found in each study: length of treatment in terms of weeks and hours and the type of treatment or teaching method under investigation. Two other variables describe study design features: sample size and outcome measure, experimenter designed or standardized. The final two variables describe the source of the study and the year of publication.
Teaching method categories were named and defined on the basis of a review of literature on algebra teaching methods and a careful reading of the studies included in the meta-analysis. Studies were grouped according to the teaching methods under investigation and category names were derived from these groupings. Categories were developed in an attempt to clearly differentiate one type of teaching method from those within other categories. Category definitions and placement of teaching methods under particular categories were tested using a content validation process. During two rounds of content validation, 14 students attending a secondary mathematics teaching methods course at Virginia Polytechnic Institute and State University during the spring of 2002, assessed each teaching method's category placement and strength of association to the category, along with its definition's clarity. (See Haas, 2002, for a more in-depth description of this process.)
Within this process, teaching methods found in nonexperimental research reports were also assessed for appropriate placement under categories in order to augment the categories for further research (Haas, 2002). These nonexperimental methods were not included in the statistical results of the meta-analysis, but they are presented in the results section of this report to give examples of teaching methods for practitioners. When a study seemed to use a combination of teaching methods, the decision for classification into a category was based on the definition of the teaching method and the purpose of the study as described by the researcher. Teaching methods outlined here should not be considered mutually exclusive because one method may contain another. For example, a problem-based learning approach to teaching may include the use of technology, such as calculators for graphing, to enhance student understanding.
