Recently researchers Scott Baker, Eugene Research Institute/University of Oregon; Russell Gersten, Instructional Research Group, Long Beach, California; and Dae-Sik Lee, Inchon (Korea) National University of Education, set out to determine which methods and practices are effective with low-achieving elementary and middle-school students. Baker et al. selected studies that targeted low-achieving math students, used randomly assigned experimental and control groups, and met standards of scientific rigor.
Of the 599 studies carried out in the past 20 years, only 15 studies met the requirements. Although the studies were few in number, the quality of the research was high.
Results indicate that there are some differences between what works best for average students and what works best for students with low achievement. Low-achieving students benefited from specific feedback about their performance, peer tutoring, computer-assisted instruction, use of parents to support math instruction, and use of explicit, teacher-facilitated instructional approaches.
Specific Feedback and Recommendations
Providing feedback and recommendations to students about their performance yielded moderately positive effects. Students who received information about their performance on math problems and who received recommendations from either their teacher or a computer program regarding the problems they need to practice outperformed students who did not receive such explicit feedback and advice.
Peer-assisted learning interventions invariably led to positive effects on student achievement. An important feature of these peer tutoring programs was that they covered material on which students had performed poorly in curriculum-based tests. Peer tutoring demonstrated a consistently positive effect on the computation abilities of low achievers. It is unclear how helpful peers may be in other areas of mathematics.
Two types of instructional practices were examined — explicit instruction and real-world problem solving. Direct, explicit instruction provides practice of a principle or concept. The effect of this focused instruction was consistently positive on the achievement of at-risk students.
Explicit strategy instruction involves the teacher’s modeling a series of questions to help students understand the problem. This leads students to decipher the vocabulary, to determine if the necessary information is available to solve the problem, and to use the correct procedure to solve the problem in a step-by-step manner. This instruction in math operations requires extensive and carefully crafted practice lessons.
Instruction in real-world applications produced mixed results. Some studies involving problems set in real-world contexts showed positive effects. On average, however, students who worked on these problems without direct, teacher-led instruction did no better than students in control groups who received text-driven instruction.
Keeping Parents Informed of Students’ Progress
The two studies that measured the effect of parents’ being kept informed of their children’s math achievement focused on improving math computational skills. Both studies produced positive effects that these researchers consider significant, given the simplicity of the intervention. All information provided to parents in these studies was positive, highlighting effort, perseverance and achievement.
Baker et al. conclude that four findings from these studies are consistent enough to be considered components of best practice. Providing students with specific information on how they are doing and recommending problems for further practice consistently enhances math achievement. Using peers as tutors enhances low achievers’ computational abilities. However, more research is needed on the ability of peers to improve problem-solving abilities. Providing clear, positive feedback to parents of low achievers seems to enhance achievement modestly.
Finally, principles of direct or explicit instruction can be useful in teaching math concepts and procedures. This includes teaching strategies as well as the more traditional direct instruction of computation and problem solving, followed by extensive practice.
There is less clarity about the effects of contextualized practice with real-world problems in which the teacher serves primarily as a facilitator. A small positive effect was found when students worked on real-world problems after they had been explicitly taught the underlying math concepts. Low achievers seem not to do as well on authentic problem solving and discussion of concepts without solid preparation in underlying math foundations.
“A Synthesis of Empirical Research on Teaching Mathematics to Low-Achieving Students” The Elementary School Journal Volume 103, Number 1, September 2002 pp. 51-73.
December 2002/January 2003 Volume 16 Number 1