Flexibility when Dealing with Situational Structures in Mathematical Contexts—A Preliminary Study Investigating a Learning Framework on Solving Additive Word Problems

Gabler, Laura; Ufer, Stefan

doi:10.1007/s13138-020-00170-3

Cited by 4 publications

(4 citation statements)

References 35 publications

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“…Word problems are called consistent, if the direct translation strategy results in a (addition/subtraction), that correct mathematical model, i.e., if the wording of the word problem (additive/subtractive) reflects the operation (addition/subtraction) that can be applied to the given numbers directly, to obtain a valid mathematical model. Consistent word problems have been found to be easier than inconsistent ones (Lewis and Mayer, 1987, "consistency hypothesis") for primary school students (Verschaffel, 1994;Gabler and Ufer, 2020) and adults (Daroczy et al, 2020). This means, for example, that the inconsistent word problem "Chris has 4 marbles.…”

Section: Additive Vs Subtractive Wording and Consistencymentioning

confidence: 99%

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I have three more than you, you have three less than me? Levels of flexibility in dealing with additive situations

Ufer,

Kaiser,

Niklas

et al. 2024

Front. Educ.

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Assessment and intervention in the early years should ideally be based on evidence-based models describing the structure and development of students’ skills. Mathematical word problems have been identified as a challenge for mathematics learners for a long time and in many countries. We investigate flexibility in dealing with additive situations as a construct that develops during grades 1 through 3 and contributes to the development of students’ word problem solving skills. We introduce the construct based on prior research on the difficulty of different situation structures entailed in word problems. We use data from three prior empirical studies with N = 383 German grade 2 and 3 students to develop a model of discrete levels of students’ flexibility in dealing with additive situations. We use this model to investigate how the learners in our sample distribute across the different levels. Moreover, we apply it to describe students’ development over several weeks in one study comprising three measurements. We derive conclusions about the construct in terms of determinants of task complexity, and about students’ development and then provide an outlook on potential uses of the model in research and practice.

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Section: Additive Vs Subtractive Wording and Consistencymentioning

confidence: 99%

“…There is evidence that, at least for young learners, word problems with unknown reference or relation set are more difficult than those with unknown result set (Gabler and Ufer, 2020;Van Lieshout and Xenidou-Dervou, 2020). One reason may be that the learners' Different semantic structures relating to the same mathematical structure.…”

Section: Unknown Setmentioning

confidence: 99%

I have three more than you, you have three less than me? Levels of flexibility in dealing with additive situations

Ufer,

Kaiser,

Niklas

et al. 2024

Front. Educ.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Stern (1998) described the ability to understand numbers as the ratio between two sets, as a concept that students must develop over time. A third reason for the difficulty that particularly applies to Grade 1 could be problems in text comprehension if the problem is presented in written form (Gabler & Ufer, 2020;Stern, 1993). An example is signal word strategies where the operation is derived directly from the wording of the problem ('less' = subtraction, 'more' = addition, Stern, 1993).…”

Section: Quantitative Comparisonsmentioning

confidence: 99%

“…A more precise analysis of students' performance should also include problems with unknown comparisons or reference sets (cf. Gabler & Ufer, 2020), including their specific difficulties and requirements. However, our measure has solid and reliable psychometric characteristics and the corresponding relation to the textbooks is explainable by the quality of learning opportunities.…”

Section: Limitationsmentioning

confidence: 99%

The role of textbook quality in first graders’ ability to solve quantitative comparisons: a multilevel analysis

Sievert

Ham

Heinze

2021

ZDM Mathematics Education

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Students need to create mental models for different types of addition and subtraction situations in order to develop a broad and viable understanding of these operations. Although most students succeed when changing or combining sets, situations that demand a quantitative comparison of sets seem considerably more difficult in the first school year. Textbooks represent the most important learning resource for elementary school mathematics teachers. However, research on their impact on students’ knowledge is limited. Hence, we examined textbooks’ role in students’ ability to model quantitative comparisons by analyzing the learning opportunities presented by four German textbooks for Grade 1 and by conducting a secondary analysis of a dataset based on 1513 students from 84 classes that used one of these textbooks. The results revealed differences in the textbooks’ topic-specific instructional quality as well as a significant relation between this quality and student achievement in quantitative comparisons.

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

Gabler

Ufer

2021

ZDM Mathematics Education

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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.

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Flexibility when Dealing with Situational Structures in Mathematical Contexts—A Preliminary Study Investigating a Learning Framework on Solving Additive Word Problems

Cited by 4 publications

References 35 publications

I have three more than you, you have three less than me? Levels of flexibility in dealing with additive situations

I have three more than you, you have three less than me? Levels of flexibility in dealing with additive situations

The role of textbook quality in first graders’ ability to solve quantitative comparisons: a multilevel analysis

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

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