The effects of using drawings in developing young children’s mathematical word problem solving: A design experiment with third-grade Hungarian students

The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students?? knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment involved five experimental and six control classes (N?=?106 and 138, respectively) of third-grade students. The experiment comprised 20 lessons with 73 word problems, providing a systematic overview of the basic word problem types. Teachers of the experimental classes received a booklet containing lesson plans and overhead transparencies with different types of visual representations attached to the word problems. Students themselves were invited to make drawings for each task, and group work and teacher-led discussion shaped their beliefs about the role of visual representations in word problem solving. The effect sizes of the experiment were calculated from the results of two tests: an arithmetic skill and a word problem test, and the unbiased estimates for Cohen??s d proved to be 0.20 and 0.62. There were significant changes also in experimental group students?? beliefs about mathematics. The experiment pointed to the possibility, feasibility, and importance of learning about visual representations in mathematical word problem solving as early as in grade?3 (around age 9?C10).     

Assessing and tracking students’ problem solving performances in anchored learning environments

The purpose of this randomized experiment was to compare the performance of high-, average-, and low-achieving middle school students who were assessed with parallel versions of a computer-based test (CBT) or a paper-pencil test (PPT). Tests delivered in interactive, immersive environments like the CBT may have the advantage of providing teachers with diagnostic tools that can lead to instruction tailored to the needs of students at different achievement levels. To test the feasibility of CBT, students were randomly assigned to the CBT or PPT test conditions to measure what they had learned from an instructional method called enhanced anchored math instruction. Both assessment methods showed that students benefited from instruction and differentiated students by achievement status. The navigation maps generated from the CBT revealed that the low-achieving students were able to navigate the test, spent about the same amount of time solving the subproblems as the more advanced students, and made use of the learning scaffolds.

A successful professional development program in history: What matters?

This study focuses on a successful Professional Development Program for improving students’ understanding of historical time, consisting of a training and the implementation of Timewise, a teaching approach in which timelines were used consistently. The PDP was carried out with 16 elementary school teachers in grades 2 (ages 7-8) and 5 (ages 10-11). Results indicate that the highest student learning gains were reached by teachers who successfully implemented the instructional behavior aimed at, while using educative curriculum materials. The clear structure of Timewise and the user-friendly materials, which included room for autonomy, supported teachers in their learning and teaching.     

Should talented students skip a grade? A literature review on grade skipping

European Journal of Psychology of Education - Since 2004, many researchers have considered that grade skipping has a positive impact on academic achievement and is not detrimental to psychosocial...     

What do employers pay for employees’ complex problem solving skills?

We estimate the market value that employers assign to the complex problem solving (CPS) skills of their employees, using individual-level Mincer-style wage regressions. For the purpose of the study, we collected new and unique data using psychometric measures of CPS and an extensive background questionnaire on employees’ personal and work history. The data were collected in 16 firms (23 establishments) in Germany, Spain, South Africa, Denmark, Slovakia, Switzerland, and France in the period 2012–2014. We find significant economic returns to CPS in our sample. One standard deviation higher CPS is associated with 10–20% higher hourly wages. The returns to CPS are sizeable even after controlling for fluid intelligence, suggesting that CPS probably captures skills important for modern production that are beyond what general intelligence tests can measure.     

What do students gain from games? Dice games vs word problems

Learning the fundamentals of probability and random variables can be a struggle for many students. Games by their nature require active participation and reward mastery, lending naturally to the framework of active learning. In this study, we designed and evaluated the efficacy of a lab activity using a game where strategy hinges on sums of dice to teach about linear combinations of independent random variables. We found that both activities lead to improved understandings of course concepts, but the dice game provided increased student engagement and interest.     

When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers’ conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe students’ strategies in situational contexts within or outside the scope of the intuitive conception. The results revealed that teachers relied on their PCK and identified student strategies; however, in the presence of the intuitive conception, their PCK was overshadowed and they ceased to differ significantly from non-teachers. This brings the attention to certain biases that can have a strong impact on teachers’ efficient use of PCK.     

Primary school students’ strategies in early algebra problem solving supported by an online game

In this study we investigated the role of a dynamic online game on students’ early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10–12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the students’ online working when solving the problems. Before and after the intervention a paper-and-pencil test on early algebra was administered. The data analysis revealed that the online working contributed to the students’ early algebra performance. There was a significant gain in performance across all grades. The highest effect was found in grade 6. Out of the three strategy profile clusters that could be distinguished in the whole sample, the cluster dominated by using extreme values and the cluster characterized by the trial-and-error strategy were most influential on the gain in early algebra performance. The students’ level of online working, which was defined as a combination of online involvement and strategy use, appeared to have a marginally significant effect on the gain score for the total sample. Per grade there was no significant effect, yet the levels of online working were significantly related to grade. Free playing was mostly performed in grade 4, looking for answers in grade 5, and exploring relations slightly more in grades 5 and 6. About 17 % of the effect of grade on the gain score was mediated by the level of online working.     

What reasons are given by teachers who refer problem behavior students?

Referral information regarding 215 students referred to school psychologists was reviewed. Of this group, 74% were males and approximately one-half were referred while enrolled in the third through sixth grades. The most frequently stated reasons for referral were: (a) poor peer relationships, (b) displays frustration, (c) below academic expectations, (d) shy and withdrawn behavior, (e) disruptive behavior, (f) fighting, (g) refuses to work, and (h) short attention span. Referral reasons presented by classroom teachers correspond to the four major characteristics of behavior disorders: conduct disorders, personality disorders, inadequacy/immaturity, and socialized delinquency. Most referrals corresponded to reported behaviors representing conduct and personality disorders.     

Confused,now what? A Cognitive-Emotional Strategy Training (CEST) intervention for elementary students during mathematics problem solving

We developed a cognitive-emotional strategy training (CEST) intervention to teach fifth-grade students (N = 57) self-regulated learning strategies that can be used when confusion is experienced during mathematics problem solving in addition to strategies they can implement during learning to help solve them. Fifth-grade students were randomly assigned to the intervention condition or the control condition. A think-emote-aloud protocol was administered to capture self-regulatory processes and emotions as students solved a complex mathematics problem. Using an explanatory mixed methods design, results revealed that, compared to students in the control condition, students who received the intervention scored significantly higher on the mathematics problem, implemented more cognitive and metacognitive learning strategies across the four phases of self-regulated learning, expressed more positive emotions and fewer negative emotions, and were better able to regulate and resolve their confusion when it occurred. These results extend previous findings from the strategy instruction literature by incorporating consideration of the role of emotions during learning.     

What is the unknown? The ability to identify the semantic role of the unknown from word problems longitudinally predicts mathematical problem solving performance

The current study aimed to investigate children’s difficulties in word problem solving through assessing their ability to mathematize, or to identify the semantic role of the unknown from word problems. Fifth graders (n = 213) were given an advanced word problem reasoning task in which they had to match word problems with schematic diagrams that depict different processes (multiplication versus division) and the unknown being in different semantic roles (e.g., unit size, number of units, or total in an equal group problem). They were also tested on their mathematical problem solving as well as some potential confounding variables (i.e., intelligence and working memory) and mediators. The ability to identify the semantic role of the unknown was shown to be longitudinally predictive of children’s mathematical problem solving performance even after controlling for the effects of covariates and autoregressor. Such a relation was partially mediated by children’s ability to convert word problems into the correct number sentences/equations. The findings not only highlight the importance of unknown identification in mathematical problem solving process, but also provide a practical tool to assess such an ability.     

What happens when students do simulation-role-play in science?

This article outlines some of the findings based on a study by three teachers and a university academic of role play in the teachers' classes. The study focuses on the results of role plays undertaken with students in mixed ability classes from three high schools in New South Wales. Role plays, where students play parts in scientific phenomena such as the electrons in an electric circuit or molecules from food in digestion, are not new to science education. But, what happens when students participate in role plays in science? In this report it is suggested that simulation-role-play may allow students to demonstrate their understanding, explore their views and develop deeper understanding of phenomena. A strategy for using analogical analysis in simulation-role play is suggested but concerns are raised about the students' capacity to distinguish role play from the subject matter being studied.     

Relationships among computational performance,pictorial representation,symbolic representation and number sense of sixth‐grade students in Taiwan

Twenty classes in ten schools with 627 sixth‐grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One‐way ANOVA analysis indicate that significant difference was found among WCT, PRT, SRT and NST tests, with F=536.327, p=0.000. The a posteriori comparisons show for each pair (WCT vs PRT, WCT vs SRT, WCT vs NST, PRT vs SRT and SRT vs NST) significant difference at the 0.001 level (p=0.000), except for the pair comparison between PRT and NST. This implies that these Taiwanese students were highly skilled in written computation but their written skills were not equally transferred to use of non‐computational paths that depended on symbolic representation, pictorial representation and number sense to solve similar problems.     

Scaffolding middle school students’ content knowledge and ill-structured problem solving in a problem-based hypermedia learning environment

This study investigated the effects of domain-general and domain-specific scaffolds with different levels of support, continuous and faded, on learning of scientific content and problem-solving. Students’ scores on a multiple-choice pretest, posttest, and four recommendation forms were analyzed. Students’ content knowledge in all conditions significantly increased from pretest to posttest. However, the continuous domain-specific condition outperformed the other conditions on the posttest. Although domain-general scaffolds were not as effective as domain-specific scaffolds on learning content and problem representation, they helped students develop solutions, make justifications, and monitor learning. Unlike domain-specific scaffolds, domain-general scaffolds helped students transfer problem-solving skills when they were faded. Several suggestions are discussed for making improvements in the design of scaffolds to facilitate ill-structured problem solving.     

What is successful adaptation of lesson study in the US?

This paper features a case study of one US K-8 school district pioneering the use of “lesson study,” a teacher professional development approach adapted from Japan. The case explores events that occurred in the district over more than 4 years (Spring 2000–Fall 2004) as lesson study spread nationally and within the district. We document four categories of changes that occurred in the district’s lesson study approach, and describe some of the early consequences of these changes as well as conditions that enabled the changes to occur. We argue that this case illustrates much of what we would hope to see in a maturing lesson study effort, and conclude that other US sites may need to go through similar changes, organize similar supports, and persist in their learning about lesson study to successfully adapt this model to their local contexts.