Addition Word Problems Research Articles

The effects of self-questioning on additive word problem solving

This study underscores the critical role of mental representation and advanced reading comprehension in solving mathematical word problems. Proficient problem solvers create nuanced mental models of problem situations, while less successful ones rely on simpler translations. Advanced reading comprehension aids in navigating the complexity of word problems, including element sequencing and semantic relations. The purpose of this study was to assess the impact of a self-questioning strategy on four elementary students’ comprehension of additive problems. These students were trained to ask questions that helped uncover semantic relations in problems. Results showed significant improvement in their ability to interpret these relations and apply the self-questioning method to comprehend two-step additive problems.

An analysis of semantic structures of addition and subtraction word problems used in primary two mathematics textbooks

In this study, addition and subtraction word problems based on the semantic structures are analyzed in the sole primary two mathematics textbooks and accompanying workbooks used in Singapore. Based on a conceptual coding framework, the word problems were coded accordingly. The results revealed a significant representation of combine and compare structures across all contents in both the textbooks and accompanying workbooks. In particular, the lack of word problems involving change structure suggests an unequal distribution of the semantic structures. Based on the findings, it is recommended that educators and textbook authors to be aware in providing students the opportunity to be equally exposed to the various semantic structures in the teaching and learning of both the addition and subtraction word problems.

Using Mixed Methods to Evaluate Modified Schema-Based Instruction in General Education Classrooms

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified concrete-semi-concrete-abstract instructional sequence. This study investigated the impact of the intervention on the word-problem-solving, strategy use, and concept acquisition of three students with extensive support needs. The paraprofessional-delivered intervention was implemented in elementary general education mathematics classrooms using embedded instruction and focused on teaching students to solve addition and subtraction word-problems. Single-subject data indicated that all three students learned to solve word-problems given concrete materials but needed more time to master the use of semi concrete supports. Qualitative data indicated that students used taught and untaught strategies to solve word-problems, and mastered addition word-problems before subtraction when they were taught simultaneously. Data were integrated in narrative format to explore how strategy use and concept acquisition related to student word-problem-solving performance. Limitations and implications for research are discussed.

Applying Problem Solving Approach in Teaching Addition and Subtraction Word Problems in Diverse Grade 3 Classrooms

Word problem solving is an approach that can increase knowledge, improve performance and develop learners’ critical thinking skills that can assist them in solving mathematical and real-life problems. This study examined the effectiveness of using a word problem solving approach to improve Grade 3 learners’ performance when learning addition and subtraction. The study employed this hypothesis to test the difference between the experimental and control groups and between the pre-test and post-test with learners in diverse classrooms solving addition and subtraction word problems. A pre-test-intervention-post-test research design was used to collect the data. Baseline lesson observations and unstructured interviews were conducted to understand the effectiveness of the problem solving approach in teaching number concepts, problems, addition and subtraction. The results of the study revealed a significant difference between the experimental and comparison groups when solving addition and subtraction word problems. Furthermore, there was a significant difference between the pre-test and the post-test in the experimental group. It was concluded that word problems could be taught by following steps for problem solving and equipping learners with essential reading skills to help them comprehend what they are reading. The interviews showed that teachers do not have enough time for learners who experience learning challenges and reading in particular in pursuit of covering the curriculum. Learners in the foundation phase must be taught money problems and problem-solving skills to acquire knowledge to be used in higher grades and real-life situations.

An exploration of grade 2 learners’ experiences in solving addition and subtraction word problems

Mathematics has always been a major part of school curricula in most countries. It provides a variety of useful tools that help students to solve problems that they encounter in everyday life. Mathematical tools are considered powerful, as long as one knows how to employ them across a range of suitable situations. However, selecting and using these tools appropriately appear to be challenging for many students. Because of this, word problems have been included in mathematics education to offer practice for students in applying mathematical skills effectively in various problem situations confronted in everyday circumstances. In addition, there is limited research about how learners in the foundation phase (Grades 1-3) solve addition and subtraction word problems. A relatively recent review of South African studies on mathematics education has revealed a paucity of research at the primary school level. This study therefore seeks to explore grade 2 learners’ experiences in solving addition and subtraction word problems. A qualitative research was conducted to describe grade 2 learners experience whilst solving addition and subtraction problems. Only 6 learners in grade 2 were selected to participate in this study. Learners demonstrated a strong preference for paper and pencil methods as well as the standard algorithm, when solving problems in word format. However, little evidence exists within the study that any of the learners conceptually understood the algorithm. The use of base 10 blocks to model the partial sums and partial differences algorithms would help most of the learners to develop a conceptual understanding of addition and subtraction of word problems in mathematics.

Effect of Model-Based Problem Solving on Error Patterns of At-Risk Students in Solving Additive Word Problems

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems due to a lack of conceptual understanding of word problem solving, which results in poor mathematics performance and falling further behind the normal achievements of their peers. Current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, including all students. The purpose of this study was to evaluate the impact of a computer-assisted model-based problem-solving intervention program (MBPS) on elementary students’ word problem-solving performance by analyzing the error patterns. Results indicate that after the MBPS intervention, participants significantly improved their problem-solving performance and made fewer errors in solving problems across a range of additive word problem situations. Specifically, the participating students made their attempt to represent the mathematical relation, decontextualized from the word problem story, in the model equation before solving the problem, rather than blindly applying an operation or relying on the “keyword” strategy as they did during the preassessment. Implications of the study are discussed in the context of the National Council of Teachers of Mathematics’ calling for teaching big ideas to help students develop a deep understanding of mathematics knowledge.

Word Problem Performance of U.S. First Graders in the 20th Century and Common Core Era

Changes in U.S. textbooks indicate that U.S. first-grade students in the Common Core era were exposed to a wider variety of word problem types than students in previous generations were. We compared the performance of U.S. first graders in the Common Core era with that of previous generations in solving 11 types of additive word problems to investigate a decades-long debate—whether certain types of word problems are inherently more difficult than others or whether relative difficulty is influenced by exposure. We found that overall patterns of relative difficulty persist; however, U.S. first graders in the Common Core era outperformed their historical counterparts when solving the types of problems that rarely appeared in textbooks used in the 1980s.

Beyond Keywords: Applying Systemic Functional Linguistics to Unpack the Language of Additive Word Problems

Beyond Keywords: Applying Systemic Functional Linguistics to Unpack the Language of Additive Word Problems

Strategies to Help Students Solve Addition and Subtraction Word Problems

Successful math word-problem solving is difficult for some students. Getting the right answer involves students engaging correctly in an amalgamation of actions. Schema instruction is an instructional approach aimed at supporting students in identifying the underlying math problem structure to yield an appropriate solution plan. The focus of this article is on supporting educators in understanding the core ingredients of schema instruction and explaining how to implement it effectively with students with elementary grades emotional and behavioral disorders.

Debugging the Underlying Cognitive Factors in Fraction Addition Word Problems

Debugging the Underlying Cognitive Factors in Fraction Addition Word Problems

Enhancing Mathematical Word Problem Solving Skills: Using Bar Model Visualization Technique

The study purpose is to investigate the effect of Bar Model Visualization Technique on the word problem solving skills of elementary level students in mathematics. Following were the objectives of the study (i) to investigate the effect of Bar Model Visualization Technique on addition word problems-solving skills; (ii) to investigate the effect of Bar Model Visualization Technique on subtraction word problems solving skills; (iii) to investigate the effect of Bar Model Visualization Technique on multiplication word problems solving skills; (iv) to investigate the effect of Bar Model Visualization Technique on division word problems solving skills. The null hypotheses were designed to test the objectives as (i) there is no significant effect of Bar Model Visualization Technique on addition word problem solving skills; (ii) there is no significant effect of Bar Model Visualization Technique on subtraction word problem solving skills; (iii) there is no significant effect of Bar Model Visualization Technique on multiplication word problem solving skills; (iv) there is no significant effect of Bar Model Visualization Technique on division word problem solving skills. The nature of the study was experimental. Pre-test and post-test equivalent group design was used as a tool for data collection in this study. Sample of the study was 40 students (Male & Female) of Government Primary School No.2 Bab-e-Jadeed District Nowshera, Khyber Pakhtunkhwa. The sample students were divided on the basis of pretest scores by applying paired random technique in to experimental group and control group. Data were analyzed by mean, SD and t-test. It was concluded that the concepts of Bar Model Visualization Technique had significant effect on addition word problems and subtraction word problems but it has not significant effect on multiplication word problems neither division word problems. The results of the study show that Bar Model Visualization Technique had significant effect on Mathematical word problem solving skills and also the learner take interest in the subject. It provides alternative method for teacher to teach mathematics subject.

Teaching Students With Mild Intellectual Disability to Solve Word Problems Using Schema-Based Instruction

This study, which used a multiple baseline across participants’ design, examines the effectiveness of a modified schema-based instructional approach to improve the mathematical word problem solving performance of three students with mild intellectual disability, two of whom had an autism spectrum disorder. Following the intervention, the three students improved their performance when solving addition and subtraction change word problems; however, their performance was inconsistent on change word problems. The effects of the instruction were generalized to two-step addition and subtraction word problems for the three participants. Moreover, the results were generalized to an untrained setting and were maintained 8 weeks after the instruction. The implications of these findings for teaching problem-solving skills to students with intellectual disability are discussed.

Addition and subtraction word problem tasks in reform‐based textbooks

AbstractOne of the factors associated with the less than positive mathematics performance of American students could be poorly designed textbooks that fail to facilitate the development of critical mathematical ideas. This study examined two reform‐based textbooks (Go math! and Investigations) in reference to essential, mathematical big ideas emphasized in the Essential Understanding Series (EU) presented by NCTM against the backdrop of mathematics education reform. In particular, we analyzed the features of the lessons for teaching addition and subtraction word problem solving. In some aspects, the results indicated that in terms of teaching problem comprehension and algebra readiness, the two textbook series showed improvement compared to formerly used textbooks. However, both textbook series may fall short of reflecting some important EU big ideas (e.g., teaching the underlying structure and part‐part‐whole relation of addition and subtraction word problems; providing students with chances to deal with exhaustive problem types and situations). In particular, our findings highlight the need for teaching word problem solving through building abstract level conceptual understanding. Implications for future textbook developing and limits are discussed.

Gaining flexibility in dealing with arithmetic situations: a qualitative analysis of second graders\u2019 development during an intervention

The influence of language and situation structure on the difficulty of word problems has been investigated intensively in the field of mathematics education. However, instructional approaches to overcoming students’ difficulties are still not widely available. This paper describes an intervention to develop second graders’ skills in handling additive word problems flexibly. During ten small-group sessions of 40 min, two strategies to restructure the situation described in a word problem were introduced: (1) changing the direction of mathematical relations and (2) changing semantic structures. The introduction of these strategies was supported using macro-scaffolding. The development of students’ flexibility in dealing with arithmetic situations during the intervention was analyzed in a longitudinal case study focusing on four students, who were preselected from a larger sample based on their language skills. We examined audio data and student work by applying qualitative content analysis. Students’ development in handling word problems flexibly was compared with the intended learning trajectory in the intervention. The results provide insights into potential key processes when gaining flexibility, and yield information on the necessary adaptations of the learning trajectory.

Can manipulatives help students in the third and fifth grades understand the structure of word problems?

Little is known about whether manipulatives can support children’s inferences of the mathematical structure of word problems. The objective was to test the effects of using manipulatives during problem solving on students’ understanding of the additive relationships in word problems. Third and fifth graders (N = 45) solved one-step addition and subtraction word problems that described either a mathematical action or relation. Children in each grade were randomly assigned to either a manipulatives or a paper-and-pencil condition. Problem structure understanding was assessed by the degree to which students’ strategies and verbal justifications reflected the quantitative relationships described in the problem text. Performance of the fifth graders was not impacted by the use of manipulatives, but in the third grade, strategy performance with manipulatives was superior to performance without manipulatives on Relation problems. The degree to which the third graders’ justifications were aligned with corresponding problem structure was positively impacted by manipulatives regardless of problem type.

Comparing the frequency and variation of additive word problems in United States first‐grade textbooks in the 1980s and the Common Core era

AbstractDecades of research conducted worldwide has resulted in a taxonomy for word problems involving additive situations. Research published in the 1980s found that U.S. curricula only exposed first‐grade students to a small subset of the easiest types of word problems. Widely adopted curriculum standards in the United States call for first‐grade students to be exposed to the full set of 11 types of problems in the taxonomy, but research shows that substantive changes to the content of instructional materials can be elusive. We asked whether the U.S. curricula continue to expose students to the same small subset of problems. We coded four widely used first‐grade textbooks from the Common Core era. Comparing our findings with those from the 1980s, we found many more word problems, a wider variety of word problems, and a consistent pattern in relative emphasis of various problems in the current textbooks. These results clearly show that U.S. students’ exposure to word problems through curriculum materials has changed. This finding lays the groundwork for further research to determine whether such changes in exposure to different types of word problems have resulted in changes to relative problem difficulty.

Teaching addition strategies to students with learning difficulties.

In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been highlighted. Observing how these strategies emerge and develop in children with learning difficulties is crucial, as it allows us to understand how they develop a subsequent understanding of arithmetic operations. In this paper we study the effect of explicit instruction in addition strategies, focusing on the minimum addend strategy, and analyze the difficulties that arise during this process. An adapted multiple-probe design across students with a microgenetic approach was employed to assess the effectiveness of the teaching instruction and the acquisition of the minimum addend strategy while solving addition word problems. The participants were three primary-school children (two boys and one girl) with learning difficulties, one of them diagnosed with autism spectrum disorder. The instruction on the minimum addend strategy was sequenced into levels of abstraction based on the addends represented with and without manipulatives. The results show that the three participants were able to acquire the minimum addend strategy and transfer it to two-step problems. They all showed difficulties during the instructional process, with quantity comparison difficulties predominating. The instruction provided to address these and other difficulties is detailed for each participant. The teaching of the minimum addend strategy has proven effective, and all three students acquired it throughout the instruction. The results concerning the student diagnosed with autism spectrum disorder are especially interesting given the lack of studies that focus on the strategies employed by students with this disorder to solve arithmetic problems. In this sense, the use of the microgenetic approach was especially useful to observe the type of spontaneous strategies used by this participant, and how they varied in response to the instruction. Each study participant faced different difficulties and needed different periods of time to assimilate the new strategy. Conclusions are drawn for educators to help children with learning difficulties advance to more sophisticated strategies, so they can acquire these and subsequent mathematical concepts.

Effect of a Method Course: Improving Prospective Elementary Teachers’ Abilities to Create Addition and Subtraction Word Problems

The purpose of this research is to explore how a method course improves prospective elementary teachers’ knowledge of various structures of addition and subtraction word problems. For this purpose, 55 prospective elementary teachers who were enrolled in a mathematics education method course were asked to pose addition and subtraction word problems before and after completion of the specific unit called “Developing Meanings for the Operations”. Problems created by participants were then analyzed and categorized in light of the theoretical frame. Repeated measure design as one of the quasi-experimental designs was used in this study to measure the effects of the instruction over time. One-way ANOVA techniques were applied for data analysis. The findings of this study suggested that although certain types of problems are extensively created by participants before starting the unit, participants created more diverse addition and subtraction word problems upon completion of the specific unit.

To add or to multiply in open problems? Unraveling children’s relational preference using a mixed-method approach

Previous research demonstrated that some children inappropriately solve multiplicative missing-value word problems additively, while others inappropriately solve additive missing-value word problems multiplicatively. Besides lacking skills, children’s preference for additive or multiplicative relations has been shown to contribute to those errors. The present research, using a mixed-method approach, investigated the nature of upper primary school children’s relational preference by empirically examining characteristics of intuitions that had been postulated previously. After administering a pre-test, selected children who preferred additive or multiplicative relations further participated in one of two studies using open problems for which both types of relations were appropriate: either a reaction time study (n = 110) in which children’s acceptance behavior and reaction times were measured or a semi-structured individual interview study (n = 18) in which their answers, verbalizations, and conviction scores were collected. Results of both studies revealed that relational preference was perseverant and exerted a coercive effect on children’s reasoning: Children mostly considered only the preferential type of relation as an appropriate answer in open problems and rejected alternative answers. Furthermore, relational preference appeared as immediate, self-evident, and certain: Children rejected the non-preferential answer more quickly than an irrelevant distractor of comparable size, experienced difficulties in justifying why they gave their preferential answer, and were very convinced of this preferential answer. While this characterization held for both relational preferences, it was especially prominent for the multiplicative one. These results not only have implications for research on and educational practice in multiplicative and additive reasoning but also for the measurement of relational preference.

The Word-Problem Solving and Explanations of Students Experiencing Mathematics Difficulty: A Comparison Based on Dual-Language Status

In mathematics, the expectation to set up and solve word problems emerges as early as kindergarten; however, many students who experience mathematics difficulty (MD) and dual-language learners often present with specific challenges in this area. To investigate why these populations experience word-problem difficulty, we examined the word, problem solving and oral explanations of third-grade dual-language learners (DLLs; n = 40) and non-DLLs ( n = 40), all of whom were identified as experiencing MD. Students solved five additive word problems and provided oral explanations of their work, which were transcribed and coded for the number of words in each explanation, type of mathematics vocabulary terms used, inclusion of correct numbers in explanations, and descriptions of addition or subtraction. We identified no significant differences in word-problem scores between DLLs and non-DLLs with MD. For both DLLs and non-DLLs, students who answered problems correctly used more words in each explanation and used more mathematics vocabulary terms within their explanations. For incorrectly answered problems, the most common mistake for both DLLs and non-DLLs involved using the incorrect operation to solve the problem.