Mathematical Word Problems Research Articles

Can prior knowledge increase task complexity? - Cases in which higher prior knowledge leads to higher intrinsic cognitive load.

Cognitive load theory assumes that the higher the learner's prior knowledge (i.e., the more expert the learner), the lower the intrinsic cognitive load (complexity) experienced for a given problem. While this is the case in many scenarios, there can be cases in which the converse is also true, resulting in more expert learners reporting higher intrinsic cognitive load than novices for the same problem. This can occur in relation to problems involving complex systems (e.g., ecological systems), for which novices' problem representations may underestimate problem complexity and therefore report lower intrinsic load than experts. This finding is borne out in the current paper. In Study 1 with 118 participants from the Black Forest area in Germany, participants with higher levels of forestry and ecological expertise evaluated a problem relating to the restructuring of the Black Forest to adapt to climate change as more complex than did novices. In Study 2 (within-subjects design, n= 66 primary-school students), we conceptually replicated this finding in a domain more typical of cognitive load theory studies, mathematics. We found that higher prior knowledge also reduced the underestimation of the complexity of 'tricky', but frequently used, mathematics word problems. Our findings suggest that cognitive load theory's assumptions about intrinsic load and prior knowledge should be refined, as there seems to exist a sub-set of problem-solving tasks for which the traditional relationship between prior knowledge and reported ICL is reversed.

Effects of Multimedia Courseware on Senior School Students’ Performance in Linear Equations involving Word Problems in Gombe, Nigeria

This study investigated the effects of multimedia courseware on senior school students’ performance in linear equations involving word problems. The study employed a quasi-experimental design to explore whether or not students taught linear-equation-word-problems using the multimedia courseware can perform better than their counterparts taught using the conventional teaching methods. It also investigated gender and score-level effects of on the students' performance. The non-randomized non-equivalent groups pre-test post-test control group design involved exposing a sample of 73 second year mathematics students (39 males and 34 females) from two co-educational senior schools in Gombe, Nigeria, to two treatments (multimedia courseware and conventional teaching) a pre-test and post-test. Two instruments (Multimedia Courseware on Linear Equation Word Problems in Mathematics (MCLEWPs) and Mathematics Performance Test on Linear Equations Word Problems (MPTLEWPs)) were developed, duly validated and approved for data collection. The reliability coefficient of MPTLEWPs was found to be 0.76. The data gathered were analyzed using a t-test and Analysis of covariance at a significance level of .05. Giving to the study's findings, there was a significant difference in the performance of students taught using multimedia courseware and those taught with conventional teaching, with those taught using multimedia courseware outperforming their counterparts (t(71) = 2.19, p<0.05); a significant difference was observed between the performance of male and female students with the males taught using multimedia courseware outperforming their female counterparts (t(27) = 2.99, p<0.05); significant differences were observed among the students in the three scoring levels (high, medium, and low) with the high scorers outperforming the others (F (2,25) = 21.64, p<0.05). The study established that Multimedia courseware enhanced students' performance in linear equation involving word problems, particularly among males and high-scoring students. It is recommended that students should be engaged in learning by using multimedia courseware that is relevant and meaningful to them on a regular basis.

Brain imaging provides insights about the interaction between instruction and diagram use for mathematical word problem solving

Diagram use is generally considered an effective strategy in solving mathematical word problems, and many teachers demonstrate the use of this strategy when they are teaching. Despite such demonstrations, however, the majority of students evidence poor, ineffective use of diagrams in problem solving. This may be due to a lack of task-appropriate instruction, but to date, there is inadequate evidence to support this idea. Therefore, the present study aimed to better understand the development of diagram use competence following the provision of task-appropriate instruction, focusing on both behavioral and neurophysiological evidence (i.e., brain activity, using functional near-infrared spectroscopy or fNIRS). Sixteen participants (mean age 15.7 years) were asked to solve mathematical word problems for which the use of tables (which is one kind of diagram) was deemed effective. Data collection progressed in three phases: (1) Pre-test without the demand for diagram use, (2) Pre-test with demand to use a table, and (3) Post-test (after participants received instruction on table use for problem solving). Although table use increased in Phase 2, it was only in Phase 3 that such use led to increases in correct answers. In Phase 3, fNIRS measurements also indicated an increase in blood flow to the frontal area (DLPFC and VLPFC) of the brain usually associated with working memory activity. These results demonstrate important neurophysiological changes resulting from task-appropriate instruction that promotes effective strategy use and improves learning performance.

Mathematical Word Problems in Adult Education: What the Research Says

Mathematical Word Problems in Adult Education: What the Research Says

Problem-appropriate diagram instruction for improving mathematical word problem solving.

The use of diagrams can be effective in solving mathematical word problems solving. However, students worldwide do not construct diagrams unprompted or have trouble using them. In the present study, the effects of problem-appropriate diagram use instruction were investigated with an adaptation of the multiple baseline design method. The instruction for using line diagrams, tables, and graphs was provided to 67 junior high school students in a staggered manner and the effects on problem solving of three different types of problems was examined. The results showed that use of problem-appropriate diagrams increased and persisted over time. More importantly, the instruction led to increases in problem solving performance and to decreases in perceived cognitive load. These findings support the argument that effective diagram use depends on the acquisition not only of declarative knowledge, but also sufficient procedural and conditional knowledge.

Mathematical and computational awareness before and after the pandemic

Mathematical thinking and computational thinking go hand in hand. Both of them are based on awareness of problem-solving. However, consciousness does not exist without a proper mental and psychological state. Formerly we examined some mathematical psychological aspects that could have an impact on both mathematical and computational problem-solving. We taught novice computational programming by solving mathematical word problems. Our first experiments were performed years before the pandemic. In this study, we present the results of a new experiment on the same topic, but this was performed during the pandemic homeschool interval. The programming environment and the teaching material were the same as before. We present our results based on our homeschool experience. We expect that the results of homeschool study groups are not worse than the results of before-pandemic study groups in reaching the aforementioned aim. The experiment proved our previous hypothesis that we can successfully teach solving mathematical word problems in a computational environment, and at the same time with the help of word problems, we can successfully teach the basic elements of computer programming.

Teaching Cartesian Product Problem Solving to Students With Autism Spectrum Disorder Using a Conceptual Model-Based Approach

Students with autism spectrum disorder frequently face challenges when learning mathematical concepts. For example, they may have difficulties solving mathematical word problems, in particular Cartesian product problems. This research is a case study with a multiple probe design in which the participants were three Spanish students diagnosed with autism spectrum disorder. A conceptual model-based problem-solving approach adapted to the characteristics of the participants was used to teach them how to solve Cartesian product word problems introduced sequentially in the instruction (first multiplication, then division, and finally both operations). The results show a functional relationship between the intervention and the students’ performance. The three participants generalized their learning to two-operation Cartesian product problems (an addition and a multiplication). Moreover, two of them retained what they learned 6 weeks after completing the instruction. The implications for teaching this and other mathematical content to students with autism are discussed.

THE LATERAL THINKING PROCESSES IN SOLVING MATHEMATICAL WORD PROBLEMS REVIEWED AT ADVERSITY QUOTIENT AND REFLECTIVE COGNITIVE STYLE

Solving word problems with a thought jump shows flexibility and the ability to use alternative procedures that are important for students to master. The thought jump is a feature of the lateral thinking process and is needed to overcome the various difficulties in solving mathematical word problems. However, lateral thinking has not been widely linked with adversity quotient and reflective cognitive style. This study aimed to describe students' lateral thinking processes in solving word problems in terms of adversity quotient and reflective cognitive style. This research is a qualitative descriptive study. The subjects in this study were junior high school students in Gowa Regency, South Sulawesi Province. The research instrument used the MFFT diagnostic test, ARP questionnaire sheet, word problem text, and interview guidelines. The results of this study indicate that climber-reflective subjects can think laterally and use them to solve the first and second-word problems well. Camper-reflective subjects can only think laterally for situations that are still within reach, while for more complicated cases, camper subjects are easily distracted and even stop solving problems. Quitter subjects solve word problems very procedurally, follow rigid algorithms, and cannot work backward when faced with difficulties.

Metacognitive strategies in solving mathematical word problems: a case of Rwandan primary school learners

This study aims to understand the use of metacognitive skills by Rwandan learners while solving mathematical word problems. We interviewed and assessed third-, fourth- and fifth-grade learners from a public primary school. The following three points emerged. First, the metacognitive skills of learners with correct answers were considerably higher than that of those with incorrect answers. Second, although there was no considerable difference in metacognitive skills between learners who answered correctly and those who did not at the stage of ‘understand the problem’, considerable differences were observed in the ‘search for solving methods’ and ‘execute the solving methods’ and ‘examine the answer’ stages. During the ‘search for solving methods’ and ‘execute the solving methods’ stage, learners who answered correctly mainly used three metacognitive skills to control their learning—‘writing the process by sentences’, ‘drawing tables’ and ‘drawing pictograms’. Third, when metacognitive skills were measured and scored, the average scores for fifth and third graders were similar. The interview revealed that the teachers of third graders taught them metacognitive strategies in mathematics lessons. It can be inferred that consequently, the metacognitive skills of third graders were raised to be as high as those of fifth graders. Although this is only a single empirical study in Rwanda, it is a major step towards improving the standard of mathematics education in African countries. In the future, similar research must be conducted in other African countries to accumulate relevant research results.

Student Errors in Mathematics Word Problem: What Can Be Learned?

This study aims to understand better student errors in solving mathematics word problems. A Word problem is a problem that has a story or arrangement based on sentences. The qualitative research approach was used. The data were collected by giving tests and interviewing two male high achievers senior high school students in mathematics. The student error analysis adopted the Newman error analysis system. The source triangulation was used to ensure the data validity. Based on the collecting data and data analysis, the decoding/reading error happened caused by students' common understanding or unfamiliarity of the mathematical terms used in the problem. The subjects showed inconsistency in interpreting problem sentences and misused mathematical symbols. Furthermore, the subject encountered difficulties with the arithmetic process, especially fractions and their operation. This research identified students' difficulties in solving problem mathematics word problems. Moreover, this research provides evidence that encourages further research on mathematical literacy, mathematical communication skills, students' arithmetic skills, and the evaluation process of the problem-solving activity.

Investigating the Effectiveness of Peer Assisted Learning Strategy in Solving Mathematical Word Problems: An Action Research with Grade Six Students

The purpose of this study was to investigate the effectiveness of peer assisted learning strategy in solving mathematical word problems of grade six in a general classroom. A pre-test and post-test experimental research design was employed involving 8 students in the control group and 8 students in the experimental group respectively. Subject achievement test was administered for both the groups to determine the differences in their learning achievements before the intervention. Peer Assisted Learning strategy (PALS) was used as an instructional strategy. Mathematical word problems solving was taught using PALS in the treatment group while the control group was taught using a conventional method. A t-test for the pre-test revealed that there was no significant mean difference between the two groups, indicating a homogenous learning ability at the beginning (p=0.802). However, the post-test analysis revealed a statistical significant difference between the mean scores of experimental group (M=19.2) than the control group (M=10.9) at p=.00, indicating the improvement of students’ mathematical word problem solving skills due to the treatment of PALS. Thus, it is commendable that PALS can be used to help develop academic and social skills.

Using Video Modeling with Augmented Reality to Teach Students with Developmental Disabilities to Solve Mathematical Word Problems

Using Video Modeling with Augmented Reality to Teach Students with Developmental Disabilities to Solve Mathematical Word Problems

Assessing Teachers’ Knowledge in Analysing Errors in Mathematical Word Problems of Ghanaian Primary School Pupils

The survey investigated teacher knowledge in analysing pupils’ wrong answer solutions in mathematical problem-solving. A sample of 205 pupils and teachers from 35 Islamic primary schools in the Greater Accra Region of Ghana were surveyed. The teachers were sampled through quota sampling, while the pupils were selected via stratified random sampling. A questionnaire and achievement test were used for the survey. Frequency count, percentage, and chi-square test were used as statistical tools for data analysis. The study found that the majority (71.4%) of the primary school teachers in the Greater Accra Region had difficulty preparing a good marking scheme. Also, more than 60% of the teachers were unable to identify and analyse the errors of pupils as well as communicate feedback on the errors. The study found no statistically significant association between knowledge of error analysis and analysing wrong answer solutions (p>0.05). This study concluded that most primary school teachers in the Greater Accra Region of Ghana do not have enough knowledge in analysing mathematical wrong answer solutions of pupils by using Newman’s model synthesis. It is recommended that mathematics teachers in Ghanaian basic schools should use Newman’s model as a standard method of analysing pupils’ work. For this reason, Ghana Education Service, Ghanaian universities, and colleges of education should include Newman’s model during the training of mathematics teachers.

Incorporating Humor into Mathematical Word Problems: Is there a Negative Effect on Students’ Performance?

Incorporating Humor into Mathematical Word Problems: Is there a Negative Effect on Students’ Performance?

Effects of affiliation-, achievement-, and power-related topics in mathematical word problems on students' performance, task-related values, and expectancies.

A motivational downturn in mathematics during secondary school has been well documented for many students. As a way to address this, creating personally relevant tasks is supposed to increase students’ motivation for mathematical tasks. According to recent research, topics relating to affiliation, achievement, and power are personally relevant for young people. Prior research showed that motive imagery in school tasks increases students’ task-related intrinsic value and success expectancies. The present study examined the effect of motive topics in word problems on students’ task performance. We contextualized mathematical tasks either with affiliation, achievement, and power topics or with neutral topics not related to motive topics. The tasks were comparable regarding their mean word count, text, and mathematical complexity. In three experimental studies (N1 = 56, N2 = 63, N3 = 62), the students solved four tasks for each motive topic and neutral tasks, respectively. The dependent variables were task performance, intrinsic values, and expectancies of success. Repeated measures analyses of variance with the four-level, within-subjects factor motive imagery revealed positive effects of motive imagery in word problems on students’ task performance. This was particularly true for achievement-related tasks compared with neutral tasks. The results also indicated slightly positive effects for affiliation-related word problems on students’ performance. In addition, the intrinsic value for affiliation-related (Experiment 1) and achievement-related tasks (Experiment 3) was higher than for neutral tasks. Power imagery did not affect students’ task performance; it negatively affected students’ intrinsic value compared with neutral tasks. Task-related success expectancies were not influenced by motive imagery. The present study replicates and extends previous findings that indicate that tasks referring to affiliation and achievement imagery are more appealing to students and can benefit their performance.

Exploring the Meaning-Making Process in Conceptual Mathematics: The Case of Linguistic Markers in Algebraic Equations

As research established, linguistic features are essential to understanding mathematical word problems, and these features are seen as a significant factor of students’ difficulty in word problems. Students are unable to translate the words into numbers or formula to work on the needed mathematical operations. This present study’s aim is two-fold. First, the analysis of the syntactic features of mathematical language is hoped to contribute to the understanding of mathematical sentence by making its lexis, syntax and semantics explicit. Second, by focusing on the linguistic markers in algebraic equation, the meaning￾making process in the mathematical language was described by determining how these linguistic markers prompted the mathematical conditions in the expressions and statements. Results show that algebraic sentences of equalities were characterized by inflectional phrase (InflP) projection, and ‘if…then’ syntax, which are considered in lexico-grammatical precision. Predication in algebraic sentence of equalities was signified essentially by the linking verb ‘is’ in definition, description and illustration frames.

Solving mathematical word problems using dynamic assessment for scaffolding construction

<span>Students need the ability to solve word problems can connect mathematics with the context of everyday life. However, students experience many difficulties and need assistance in the form of scaffolding can to solve word problems well. Dynamic assessment is an alternative approach to constructing the form of scaffolding that student need to solve mathematical word problems. This study aimed to analyze the students' difficulties in solving word problems and the required form of scaffolding through dynamic assessment. The subjects of this study consisted of 177 students spread across 10 public junior high schools in Jeneponto Regency, South Sulawesi Province, Indonesia. There was a four-word problem tested and analyzed using dynamic assessment. Student solutions were grouped based on the type and form of scaffolding needed: level 5 (no solution), level 4 (without analysis/unrepresentative), level 3 (computational error), level 2 (incomplete procedure), level 1 (lack of thoroughness in the final stage). The form of scaffolding is constructed to help students solve mathematical word problems step by step at each level. The use of scaffolding accompanied by instructions helps students develop word problem-solving skills. Dynamic assessment can be considered to be integrated with the mathematics learning process that supports scaffolding construction to solve students' word problems.</span>

Attitude of class nine and ten students towards solving mathematical word problems

The study was conducted to understand the attitude towards solving mathematical word problems of 483 class nine and ten students. The quantitative method was used with purposive sampling, including all the students. Survey questionnaires with a five-point Likert scale were validated through pilot testing with 20 students and obtained a Cronbach’s alpha of 0.88. Views of students on attitude towards solving word problems, motivation of students, and implication of language in solving word problems were collected. MS Excel’s data analysis tool was used to analyze data using percentages, frequencies, descriptive analysis, and correlation. Paired t-test for the sample mean was used to see the significance of gender difference. The findings revealed a high positive attitude towards solving word problems. Students were motivated to solving word problems, the teacher is rated as the source of motivation. There was a high positive correlation between language and their love for solving mathematical word problems. There was no significant gender difference observed in attitude and motivation but gender difference was significant in the importance of language in solving word problems. Male students had a stronger belief than a female that language plays a vital role in one’s efficacy in solving mathematical word problems. Recommendations are suggested to the subject teachers to enable them to develop better instructions based on reflection.

Emergent math difficulties among English learners: can the odds be reduced?

ABSTRACT Solving word problems in mathematics presents difficulties for many English learners (ELs), including those who use Spanish as a home language. In the early stage of learning to solve mathematics word problems, some children, including ELs, experience difficulties. By English status, EL refers to those children whose home language was Spanish while in the process of developing English at school. Math difficulties (MD) refers to those children with low normative mathematical problem-solving scores in both English and Spanish. The purpose of this study was to determine those measures that increase the odds of identifying EL children with emergent MD. Elementary school children (grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, working memory [WM]) in both Spanish (L1) and English (L2) in Year 1 and again one year later. Multilevel growth modeling compared MD children identified one year later who manifested MD to children who were average math achievers or poor math achievers across the two testing waves (year 1 and year 2). The results indicated that significant growth parameters (i.e., measures of estimation, WM) increased the odds of identifying emergent MD relative to children with Persistent math deficits and average achievers. The results were discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the odds of identifying later math difficulties.

Efficacy of Peer-Delivered Mathematical Problem-Solving Instruction to Students With Extensive Support Needs

Mathematical problem solving has been identified as one foundational area of mathematics for all students but is an area of weakness for students with disabilities. This investigation sought to determine the effects of peer-delivered schema-based instruction on the mathematical problem solving of the change problem type with four middle school students with extensive support needs using a single-case multiple-probe-across-participants design. We also wanted to determine if same-age peer tutors who received behavior skills training could deliver the academic instruction with fidelity. Students and peer tutors were representative of diverse backgrounds. Results showed a functional relation between peer-delivered modified schema-based instruction and students’ acquisition and maintenance of mathematical word problem–solving skills, and strong effect sizes were found. Peer tutors were able to provide instruction with high levels of fidelity across the study. Social validity data showed that all participants benefited from the peer-delivered instruction.