Technology-enhanced mathematics instruction: A second-order meta-analysis of 30 years of research

It is important to assess the cumulative effects of technology on student achievement captured in the last 30 years of technologyenhanced mathematics instruction. Synthesizing the thousands of articles and gray literature on this subject is necessary but would require a considerable commitment of academic resources. A second-order metaanalysis or meta-analysis of meta-analyses is an alternative that is reasonable and effective. Thus, a second-order meta-analysis of 19 prior meta-analyses with minimum overlap between primary studies was conducted. The results represent 663 primary studies (approximately 141,733 participants) and 1,263 effect sizes. The random effects' mean effect size of .38 was statistically significantly different from zero. The results provide a historical and contextualized summary of 30 years of meta-analytic research, which supports meta-analytic thinking and better interpretation of future effect sizes. Results indicate that technology function and study quality are major contributors to effect size variation. Specifically, computation enhancement technologies were most effective, while studies that examine combinations of enhancements were least effective. Implications for technology-enhanced mathematics instruction and meta-analytic research are provided.     

Learner preferences and prior knowledge in learner-controlled computer-based instruction

This study examined the effects of prior knowledge, learner preference for control, and type of control (learner or program) on the achievement of middle-school students in a computer-based instructional program on adding and subtracting integers. Students were blocked by preference-for-control scores and randomly assigned to either a learner-control or program-control version of instruction. A significant three-way interaction (prior knowledge × preference scores × type of control) revealed that students with high prior knowledge achieved better on the posttest when their preference for control was matched with the type of control they received, whereas students with low prior knowledge achieved better when their preference was mismatched. A significant three-way interaction on attitude reflected the same pattern found in the interaction for achievement scores. The overall results indicate that matching learner preference to the type of program they receive is an effective strategy for high-prior-knowledge students but not for those with low prior knowledge.

Influence of instruction in mathematics for low performing students on strategy use

Effects of two subtraction instruction types for low achieving children were compared. The first was based on constructivist ideas. The second was more or less traditional but did include interaction opportunities comparable to those in constructivist classrooms. Sixteen students (eight in each condition) with an average age of 10.5 years were trained during 34 lessons. Results showed no performance differences between the two groups on the subtraction problems instructed. There was a performance advantage for the traditional group on transfer problems without regrouping. The constructivist group used more different strategies but was not able to use this bigger repertory in a flexible way; instead, they used their strategies rather randomly. These findings pose questions on the usefulness of constructivist teaching in mathematics for low performers.     

Effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers

An experiment was conducted to examine the effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers at a middle school in the North‐West Province of South Africa. Forty standard (std) 7 pupils were identified whose non‐verbal general ability and previous mathematics achievements were significantly lower than those of other std 7 pupils. These subjects were randomly assigned to an experimental group and a control group. Metacognitive strategies in solving mathematical problems related to four mathematics topics were individually taught to the members of the experimental group, while the pupils in the control group were taught the four mathematics topics through the conventional method of teaching mathematics. The comparisons of pretest and posttest measures of general ability, metacognitive awareness, attitude towards mathematics, and mathematics achievement revealed that the posttest scores of all the four variables for the experimental group were significantly higher than those for the control group.     

Immediate and delayed effects of meta-cognitive instruction on regulation of cognition and mathematics achievement

The present study addressed two research questions: (a) the extent to which students who were exposed to meta-cognitive instruction are able to implement meta-cognitive processes in a delayed, stressful situation, in our case—being examined on the matriculation exam; and (b) whether students preparing themselves for the matriculation exam in mathematics, attain a higher level of mathematics achievement and meta-cognitive awareness (knowledge about cognition and regulation of cognition) as a result of being exposed to meta-cognitive instruction. Participants were 61 Israeli high school students who studied mathematics for four-point credit on the matriculation exam (middle level). About half of the students (N = 31) were assigned to meta-cognitive instruction, called IMPROVE, and the others (N = 30) studied with no explicit meta-cognitive guidance (control group). Analyses included both quantitative and qualitative methods. The later was based on students’ interviews, conducted about a couple of months after the end of the intervention, immediately after students completed the matriculation exam in mathematics. Results indicated that IMPROVE students outperformed their counterparts on mathematics achievement and regulation of cognition, but not on knowledge about cognition. Furthermore, during the matriculation exam, IMPROVE students executed different kinds of cognitive regulation processes than the control students. The theoretical and practical implications of the study are discussed.     

Achievement goals,academic self-concept,and school grades in mathematics: Longitudinal reciprocal relations in above average ability secondary school students

This study examined the longitudinal reciprocal relations between academic self-concept, achievement goals (i.e., performance-approach, performance-avoidance, and mastery), and achievement (i.e., self-reported grades) in mathematics. The research aim was twofold. First, we examined the confound hypothesis, which states that performance-approach goals do not feature any incremental validity in predicting achievement over and above students' competence perceptions (i.e., academic self-concept). In addition, we expanded research on the confound hypothesis by also investigating performance-avoidance and mastery goals. Second, we investigated the predictive validity of all three achievement goals for changes in academic self-concept. Seven hundred sixty-nine students (50.78% female) attending the highest track of the German three-tier secondary school system participated in three waves of measurement in Grades 5, 6, and 8. Our findings confirmed the confound hypothesis: Performance-approach goals did not explain achievement over and above academic self-concept. The same findings applied to performance-avoidance and mastery goals. Furthermore, performance-approach goals were positively related to academic self-concept changes, whereas performance-avoidance goals showed a negative relation to academic self-concept changes over time. Mastery goals were not associated to changes in academic self-concept. Academic self-concept and achievement showed positive reciprocal relations. To conclude, our results point to complex relations between achievement goals, academic self-concept, and academic achievement over time.     

The effect of spreadsheet and dynamic geometry software on the achievement and self-efficacy of 7th-grade students

Background

Since the early 1980s, there has been a growing interest in the potentiality of computers as facilitators of students' learning. The importance of using technology effectively as a learning tool has been emphasized by many researchers. However, finding good software that encourages pupils to explore and express mathematical ideas is becoming a crucial issue.

Purpose

This paper investigates the effect of spreadsheet and dynamic geometry software on the mathematics achievement and mathematics self-efficacy of 7th-grade students. The study further examines the gender differences with respect to computer self-efficacy, mathematics self-efficacy and mathematics achievement. The relationship among these three constructs is also investigated.

Sample

The study consisted of 64 7th-grade students from three different classes including all the 7th- graders in a school, which is located in an upper-middle-class area in Ankara, Turkey. Study participants were aged from 12 to 13. In total, the number of female and male students was equal. In this study, purposive sampling was used since the school where the study took place was well equipped in terms of computer laboratories and technological devices.

Design and methods

The evaluation used an experimental design where two software programs, Excel and Autograph, were used in experimental groups separately, and a control group took traditional-based instruction without using any technological tools such as a computer or calculator. The study was carried out during the spring semester of the 2001/02 academic year, where three instructional methods of study: Autograph-based instruction, spreadsheet-based instruction and traditionally based instruction, were randomly assigned to the three classes. The Mathematics achievement test was used to assess the students' performance on mathematics. In order to determine the self-efficacy expectation of the students with respect to mathematics and computers, a Mathematics self-efficacy scale and Computer self-efficacy scale were developed respectively. Analysis of covariance, bivariate correlations and t-test were used to analyse outcome data.

Results

Results revealed that the Autograph group and Traditional group had significantly greater mean scores than the Excel group with respect to mathematics achievement. The Autograph group had significantly greater mean scores than the Traditional group, while no significant mean difference was found between the Autograph and Excel groups and between the Excel and Traditional groups with respect to mathematics self-efficacy. No significant mean difference was found between boys and girls with respect to mathematics achievement and mathematics self-efficacy. On the other hand, boys had significantly greater mean scores than girls with respect to computer self-efficacy. In addition, significant correlations were found among efficacy scores and achievement.

Conclusions

The evidence suggests that students showed great enthusiasm for Autograph. Students in the Autograph group had the highest scores compared to other groups regarding mathematics achievement and mathematics self-efficacy. In addition, boys reported significantly higher scores with respect to computer self-efficacy where, during the Autograph-based instruction and spreadsheet-based instruction, boys were more willing to solve activities using computers compared to girls. On the other hand, treatments seemed not to have any effect on gender regarding mathematics self-efficacy and mathematics achievement.     

Learning from instruction: the case of mathematics

Starting from a brief analysis of adaptive competence in mathematics, this article describes a series of research-based characteristics of the kind of learning processes that should be elicited in students to facilitate and support in them the progressive acquisition of such competence. Four major characteristics are discussed in some detail: learning is constructive, self-regulated, situated or contextual, and collaborative. A rather new approach to transfer of learning is then presented in which transfer is conceived as the preparation for future learning. Throughout the article it is argued that, notwithstanding the progress made in research on learning from instruction, numerous and complex issues and problems remain for continued inquiry.     

Teaching practices in Grade 5 mathematics classrooms with high-achieving English learner students

Teachers need more clarity about effective teaching practices as they strive to help their low-achieving students understand mathematics. Our study describes the instructional practices used by two teachers who, by value-added metrics, would be considered “highly effective teachers” in classrooms with a majority of students who were English learners. We used quantitative data to select two fifth-grade classrooms where students, on average, made large gains on a mathematics achievement test, and then examined teaching practices and contextual factors present in each classroom. Participants included two teachers from a mid-Atlantic district and their students who were 67% English learners and 68% economically disadvantaged. We found that the use of multiple representations of mathematics concepts, attention to vocabulary building, individual and group checks for understanding and error analysis were prevalent practices in both high gains classrooms. Also, class sizes ranged from 12–19 students. Discussion focuses on whether observed practices are aligned with recommended teaching practices for English learner students.     

Teaching for understanding and/or self-regulated learning? A video-based analysis of reform-oriented mathematics instruction in Switzerland

In mathematics instruction, can a teacher implement surface features of instruction that foster self-regulated learning as well as achieve quality at the deeper level of instruction, that is, focus on higher-order thinking, problem-solving, and mathematical modeling? An educational reform effort in Switzerland, which is based on constructivist and sociocultural theories of mathematics learning, targets both these dimensions: self-regulated learning and conceptual understanding. We examined the realization of the two dimensions in classroom instruction in a video-based study of 79 eighth-grade math classes using three kinds of data: videotapes of mathematics lessons, student and teacher questionnaires, and achievement tests. As to the surface level of instruction, teachers reported how frequently they provided opportunities for self-regulated learning. With regard to the deeper level of instruction, teachers reported how frequently they provided opportunities for independent problem solving. In addition, we examined the extent to which teachers’ pedagogical beliefs reflected a constructivist orientation. The results showed that teachers implemented the two dimensions relatively independently of one another. Teachers’ constructivist-oriented beliefs influenced only opportunities provided for independent problem solving and did not affect opportunities for self-regulated learning. Opportunities for self-regulated learning had a positive effect on students’ learning experience. Professional development should encourage teachers to take greater account of both surface-level and deeper-level (quality) features of instruction.     

Factors predictive of mathematics achievement in kindergarten,first and third grades: An opportunity–propensity analysis

A secondary analysis of the Early Childhood Longitudinal Study – Kindergarten Sample (N = 17,401) was conducted to determine the factors that are most strongly associated with math achievement during kindergarten, first grade, and third grade. Factors from the following three categories were considered: antecedent factors (e.g., family socio-economic status), opportunity factors (e.g., frequency of being exposed to mathematical content), and propensity factors (e.g., pre-existing mathematics skills). Structural equation modeling showed that math achievement was strongly predicted by a combination of specific propensity, opportunity, and antecedent factors. However, propensity factors were the most important determinants of achievement. The amount of variance accounted for by gender and ethnicity was substantially reduced when other factors in the antecedent, opportunity, and propensity categories were controlled. The implications of the findings for intervention are discussed.     

Constructivist mathematics education for students with mild mental retardation

This study examined the effects of a constructivist mathematics intervention for students with mild mental retardation, as compared to direct instruction, which is often recommended for these children. A total of 69 students from elementary schools for special education participated in the study, which focused on multiplication learning. They received one of two kinds of mathematics intervention, guided or directed instruction. Multiplication automaticity and ability tests were administered before and after the four-month training period. The results show that students in both conditions improved significantly during the training period. However, students who received directed instruction showed greater improvement than students who had received guided instruction. These results show that students with MMR can profit from constructivist instruction, although direct instruction seems more effective.     

First-graders’ knowledge of multiplicative reasoning before formal instruction in this domain

Our study investigated children’s knowledge of multiplicative reasoning (multiplication and division) at the end of Grade 1, just before the start of formal instruction on multiplicative reasoning in Grade 2. A large sample of children (N = 1176) was assessed in a relatively formal test setting, using an online test with 28 multiplicative problems of different types. On average, the children correctly answered more than half (58%) of the problems, including several bare number problems. This indicates that before formal instruction on multiplicative reasoning, children already have a considerable amount of knowledge in this domain, which teachers can build on when teaching them formal multiplication and division. Using analysis of variance and cross-classified multilevel regression analysis, we identified several predictors of children’s pre-instructional multiplicative knowledge. With respect to the characteristics of the multiplicative problems, we found that the problems were easiest to solve when they included a picture involving countable objects, and when the multiplicative situation was of the equal groups semantic structure (e.g., 3 boxes of 4 cookies). Regarding student characteristics, pre-instructional multiplicative knowledge was higher for children with higher-educated parents. Finally, the mathematics textbook used in school appeared to have influenced children’s pre-instructional multiplicative knowledge.     

Success in mathematics within a challenged minority: the case of students of Ethiopian origin in Israel (SEO)

Many studies have reported on the economical, social, and educational difficulties encountered by Ethiopian Jews since their immigration to Israel. Furthermore, the overall academic underachievement and poor representation of students of Ethiopian origin (SEO) in the advanced mathematics and science classes were highlighted and described. Yet, studies focusing on differential achievements within SEO and on students who succeed against all odds are scarce. In this study, we explored success stories of five SEO studying in a pre-academic program at a prestigious technological university in Israel. Our goal was to understand how these students frame and interpret their success in mathematics and to identify elements perceived as fostering their mathematics and academic trajectories. Using qualitative methodology, we identified perceived personal motivational variables, effective learning and coping strategies, and students’ immediate environment as key elements contributing to achieving and maintaining success. We discuss possible theoretical contributions and practical implications of the findings. This research is supported in part by the Abraham and Sonia Rochlin Foundation and by a grant from the Israel Ministry of Absorption. The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the funding agencies.     

Process matters: Teachers benefit their classrooms and students when they deliver an identity-based motivation intervention with fidelity

Students value school success but often experience classroom norms implying that learning is easy and succeeding in school is not difficult. Applying an identity-based motivation (IBM) lens highlights three ways succeed-with-ease-not-effort norms can undermine students’ grades and increase their risk of course failure. Succeed-with-ease-not-effort norms reduce the likelihood that students experience school as relevant to their future goals, experience right now as the time to get going, and difficulties as signals of schoolwork's importance, not its impossibility. To support student academic outcomes, we examine Pathways-to-Success, a classroom-level intervention operationalizing IBM theory in a 3-cycle, 3-year development design (N = 1142 8th-graders, 87% low-income families, 64% Latinx, 20% African American). We document that Pathways-to-Success can be sustainable; our middle school teachers implemented and taught other teachers to implement Pathways-to-Success. We use structural equation models to show that effects are due to the theorized process; teachers who implemented with more signal clarity supported academic success by bolstering their students' identity-based motivation. We operationalized signal clarity as a mean of five fidelity components (dosage, adherence, quality, responsiveness, receipt). Signal clarity matters; students experiencing Pathways-to-Success with a clearer signal have a higher identity-based motivation score. Higher identity-based motivation yields better school outcomes.     

Relations between mathematics achievement growth and the development of mathematics self-concept in elementary and middle grades

Creating an educational program that results in positive science, technology, engineering, and mathematics or STEM-oriented outcomes for all students is an important education objective and federal policy directive in the United States. In addition to developing strong mathematics foundations in Grades K–8 that are closely associated with successful STEM outcomes, intrapersonal skill development is also critical to academic and postsecondary success. Using nationally representative data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 the current study applied structural equation growth modeling to examine relationships among mathematics achievement in Grades K–1 and Grades 3–8, and mathematics self-concept development across Grades 3–8. Study results revealed that students reported declining levels of mathematics self-concept across the middle grades. Importantly, third grade reports of self-concept were associated with both mathematics achievement at kindergarten entry and third grade mathematics achievement; however, mathematics achievement at kindergarten entry was also associated with the development of mathematics self-concept in third through eighth grade. In addition, after accounting for mathematics achievement in Grades K–1, mathematics achievement growth in Grades 3–8 was directly associated with mathematics self-concept development across the same time period. Implications for future research, mathematics instruction, and curriculum development are discussed.     

Improving mathematics instruction through lesson study: a theoretical model and North American case

This article presents a theoretical model of lesson study, an approach to instructional improvement that originated in Japan. The theoretical model includes four lesson study features (investigation, planning, research lesson, and reflection) and three pathways through which lesson study improves instruction: changes in teachers’ knowledge and beliefs; changes in professional community; and changes in teaching–learning resources. The model thus suggests that development of teachers’ knowledge and professional community (not just improved lesson plans) are instructional improvement mechanisms within lesson study. The theoretical model is used to examine the “auditable trail” of data from a North American lesson study case, yielding evidence that the lesson study work affected each of the three pathways. We argue that the case provides an “existence proof” of the potential effectiveness of lesson study outside Japan. Limitations of the case are discussed, including (1) the nature of data available from the “auditable trail” and (2) generalizability to other lesson study efforts.

Family and motivation effects on mathematics achievement: Analyses of students in 41 countries

This study examines family and motivation effects on student mathematics achievement across 41 countries. The Rasch estimates of PISA mathematics test scores and questionnaire responses of 107,975 15-year-old students were analyzed via multilevel analyses. Students scored higher in richer or more egalitarian countries; when living with two parents, without grandparents, with fewer siblings (especially fewer older siblings); with higher family SES, more books, cultural possessions, or cultural communication; or when they had greater interest in mathematics, more effort and perseverance, and higher self-efficacy or self-concept. Family structure effects were stronger in individualistic or richer countries. Richer countries showed stronger family cultural communication effects, suggesting stronger, intangible resource effects.     

The effect of information mapping strategy on mathematics conceptual knowledge of junior high school students

The purpose of this study was to determine the effect of information mapping strategy on mathematics conceptual knowledge of junior high school students in Rokan Hulu Riau, Indonesia. The study also examined the relationship between mathematics conceptual knowledge and mathematics achievement. Using a quasi-experimental method, the study was carried out on 132 students from one junior high school in Rokan Hulu Riau, Indonesia. It was completed in 6 weeks. Instruments used in this study were mathematics conceptual knowledge test and mathematics achievement test. The results of this study indicated that there were significant differences in mathematics conceptual knowledge between the information mapping strategy group and the traditional group. It was concluded that using information mapping strategy may impact students＇ conceptual knowledge. There was a relationships between mathematics conceptual knowledge and mathematics achievement.     

在数学课上率先实行双语教学的可行性研究

本文分析了在数学课上实行双语教学的必要性和所具有的各种优势条件，提出率先在数学课上实行双语教学不仅是必要的，而且是可行的。