Dake Zhang

A Follow-Up Meta-analysis for Word-Problem-Solving Interventions for Students with Mathematics Difficulties

ABSTRACT Following a meta-analysis study conducted by Y. P. Xin and A. Jitendra (1999), the authors carried out a follow-up meta-analysis of word problem-solving interventions published from 1996 to 2009 for students with learning problems in mathematics. The authors examined the influence of education reforms as moderator variables on intervention effects, including inclusive movement, response to intervention model, standard movement, and mathematics education reform. The researchers analyzed 29 group-design studies and 10 single-subject-design studies that met the criteria for inclusion. Separate analyses were performed for group-design studies and single-subject studies using standardized mean change and percentage of nonoverlapping data (PND), respectively. The overall mean-weighted effect size (d) and PND for word problem-solving instruction were positive across the group-design studies (d = 1.848) and single-subject studies (PND = 95%). Implications for policymakers and researchers were discussed within the contexts of inclusive education, standard based movement, the response to intervention model, and mathematics education reform.

Transition From Intuitive to Advanced Strategies in Multiplicative Reasoning for Students With Math Difficulties

This study explored how a teaching experiment, which taught double counting with a constructive task assignment according to an ongoing assessment, helped students with mathematics difficulties develop their multiplicative reasoning skills. The participants were two fifth graders with math learning disabilities and one at risk. A micro-genetic approach with a single-participant design was used. Investigators coded and analyzed four strategies the children used. Results showed that unitary counting was dominant during the baseline sessions. During the teaching experiment, a great increase in the use of double counting and an obvious decrease in the use of unitary counting was observed. The participants’ improvement in problem-solving accuracy on the posttest validated their strategic development. Implications are discussed in the context of employing strategic changes as a measure for assessing students’ academic achievement and interventions for helping children adopt advanced strategies.

Pinyin Invented Spelling in Mandarin Chinese-Speaking Children With and Without Reading Difficulties

This study examined analytical pinyin (a phonological coding system for teaching pronunciation and lexical tones of Chinese characters) skills in 54 Mandarin-speaking fourth graders by using an invented spelling instrument that tapped into syllable awareness, phoneme awareness, lexical tones, and tone sandhi in Chinese. Pinyin invented spelling was significantly correlated with Chinese character recognition and Chinese phonological awareness (i.e., syllable deletion and phoneme deletion). In comparison to good and average readers, poor readers performed significantly worse on the invented spelling task, and a difference was also found between average and good readers. To differentiate readers at different levels, the pinyin invented spelling task, which examined both segmental and suprasegmental elements, was superior to the typical phonological awareness task, which examined segments only. Within this new task, items involving tone sandhi (Chinese language changes in which the tones of words alter according to predetermined rules) were more difficult to manipulate than were those without tone sandhi. The findings suggest that this newly developed task may be optimal for tapping unique phonological and linguistic features in reading of Chinese and examining particular tonal difficulties in struggling Chinese readers. In addition, the results suggest that phonics manipulations within tasks of phonological and tonal awareness can alter their difficulty levels.

Improving Multiplication Strategic Development in Children With Math Difficulties

The purpose of the present study was to examine the effectiveness of a strategic training program for improving students’ performance in solving multiplication problems. The participants were 3 third graders with math difficulties. In this teaching experiment, microgenetic analysis was used to analyze improvement in students’ strategic development and problem-solving accuracy. The instructional components included selective task assignment and OFSD (encouraging students to use Own strategy to solve problems, providing Feedback, asking for students’ Self-explanations, and explicit Demonstration of strategies when needed). The results showed that the three participants began the intervention at different strategic developmental levels and consequently were given differentiated tasks to promote their strategic development during the intervention. In response to the intervention, the three participants improved their problem-solving accuracy, use of advanced strategies, and flexibility in choosing backup strategies.

Strategic Development for Middle School Students Struggling With Fractions Assessment and Intervention

Research has suggested that different strategies used when solving fraction problems are highly correlated with students’ problem-solving accuracy. This study (a) utilized latent profile modeling to classify students into three different strategic developmental levels in solving fraction comparison problems and (b) accordingly provided differentiated strategic training for students starting from two different strategic developmental levels. In Study 1 we assessed 49 middle school students’ performance on fraction comparison problems and categorized students into three clusters of strategic developmental clusters: a cross-multiplication cluster with the highest accuracy, a representation strategy cluster with medium accuracy, and a whole-number strategy cluster with the lowest accuracy. Based on the strategic developmental levels identified in Study 1, in Study 2 we selected three students from the whole-number strategy cluster and another three students from the representation strategy cluster and implemented a differentiated strategic training intervention within a multiple-baseline design. Results showed that both groups of students transitioned from less advanced to more advanced strategies and improved their problem-solving accuracy during the posttest, the maintenance test, and the generalization test.

Testing Accommodation or Modification? The Effects of Integrated Object Representation on Enhancing Geometry Performance in Children With and Without Geometry Difficulties

According to the National Council of Teachers of Mathematics, geometry and spatial sense are fundamental components of mathematics learning. However, learning disabilities (LD) research has shown that many K–12 students encounter particular geometry difficulties (GD). This study examined the effect of an integrated object representation (IOR) accommodation on the test performance of students with GD compared to students without GD. Participants were 118 elementary students who took a researcher-developed geometry problem solving test under both a standard testing condition and an IOR accommodation condition. A total of 36 students who were classified with GD scored below 40% correct in the geometry problem solving test in the standard testing condition, and 82 students who were classified without GD scored equal to or above 40% correct in the same test and condition. All students were tested in both standard testing condition and IOR accommodation condition. The results from both ANOVA and regression discontinuity (RD) analyses suggested that students with GD benefited more than students without GD from the IOR accommodation. Implications of the study are discussed in terms of providing accommodations for students with mathematics learning difficulties and recommending RD design in LD research.

Strategies Students With and Without Mathematics Disabilities Use When Estimating Fractions on Number Lines

We examined faulty strategies with possible underlying misconceptions, as well as execution mistakes, among middle schoolers with and without mathematics disabilities when estimating fractions on number lines. Fifty-one middle schoolers participated in this study, including 27 students with mathematics disabilities. Participants were asked to estimate 10 fractions on a 0-1 number line and 11 fractions on a 0-5 number line and explain their procedures. We identified two incorrect strategies (i.e., not-on-the-line and ruler-tick-mark counting strategy) and two execution mistakes (i.e., unequal segmentation based on denominator and inaccurate numerical transformation) on both number-line estimation tasks. We also identified one additional faulty strategy (i.e., treating 0-5 as the 0-1 number line) with the 0-5 number-line estimation tasks. Students with mathematics disabilities were significantly more likely to use the faulty strategies than students without mathematics disabilities. The faulty strategies, rather than execution mistakes, were consistent across two number-line tasks and predicted students’ performance in other fraction problem-solving tasks. Results illustrated specific problems that students with and without mathematics disabilities encountered when using number lines to illustrate fractions. We discussed possible negative influences of using rulers to teach fractions and how to help students to construct the concept of units.

Working memory load and automaticity in relation to mental multiplication

ABSTRACT The authors’ aim was to examine the relations among mental multiplication, working memory load (WML), and automaticity by alternating the difficulty level of task characteristics. In Experiment 1, involving 30 fifth-grade students with mixed abilities, a 2 (WML) × 2 (automaticity) design was utilized. In Experiment 2, involving 21 high-achieving mathematics learners and 21 low-achieving mathematics learners in Grade 4, a 2 (WML) × 2 (automaticity) × 2 (achievement) design was utilized. Regardless of level of automaticity, individuals under low-WML conditions performed more accurately and faster. Regardless of level of WML, individuals under high automaticity conditions performed more accurately and faster. Group difference was significant. The simple effect of WML was bigger under the conditions with low automaticity, in comparison to the conditions with high automaticity. Alternating difficulty level simultaneously in 2 dimensions of testing conditions posed an amplified impact on the low-achieving group.

A Review of Literature:Mathematics Instruction for Students with Visual Impairments

All students, including students with visual impairments (VI), are expected to master basic mathematics skills and apply such skills to solve real life problems. In the present study, we conducted a literature review of current intervention methodologies to assist students with VI to learn mathematics. A systematic review of literature yielded 5 studies, and all are single-case studies published after 2010s. Two trends in intervention methods emerged: (1) technological interventions, which used audio devices as aids for mathematics problem-solving and (2) humandelivered cognitive interventions, which focused creating specialized instruction for educators to better suit the needs of individuals with VI. The significance and limitations of current research and recommendations for future research are discussed.

Effect of an Intervention on Conceptual Change of Decimals in Chinese Elementary Students: A Problem-Based Learning Approach

The purpose of this study was to compare a problem-based learning (PBL) approach and a traditional approach for teaching decimal concepts to 76 Chinese fifth graders. Students in the experimental group (n = 38) learned multiplication and division of decimals and word-problem solving of decimals using a PBL approach. In comparison to the control group (n = 38), students in the experimental group demonstrated significantly better performance on both mixed computation and decimal computation, provided more strategic interpretations of strategy use reflecting conceptual change, and made fewer errors when applying rules of whole number computation to decimal computation. Students in the experimental group also reported higher levels of social self-efficacy and academic interest.