Developing students’ ability to solve word problems through learning trajectory-based and variation task-informed instruction

ZDM ◽  
2018 ◽  
Vol 51 (1) ◽  
pp. 169-181 ◽  
Author(s):  
Rongjin Huang ◽  
Qinqiong Zhang ◽  
Yu-ping Chang ◽  
Dovie Kimmins
Keyword(s):  
Word Problems ◽  
Learning Trajectory ◽  
Informed Instruction

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

ZDM ◽  
2021 ◽  
Author(s):  
Laura Gabler ◽  
Stefan Ufer
Keyword(s):  
Word Problems ◽  
Qualitative Content Analysis ◽  
Second Graders ◽  
Learning Trajectory ◽  
Longitudinal Case Study ◽  
Student Work ◽  
Yield Information ◽  
Audio Data ◽  
Larger Sample

AbstractThe 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.

scholarly journals The Learning Trajectory Construction of Elementary School Students in Solving Integer Word Problems

2022 ◽  
Vol 9 (1) ◽  
pp. 404-424
Author(s):  
Andi SAPARUDDİN NUR ◽  
Kartono KARTONO ◽  
Zaenuri ZAENURİ ◽  
Rochmad ROCHMAD
Keyword(s):  
Elementary School ◽  
Elementary School Students ◽  
Word Problems ◽  
Learning Trajectory ◽  
School Students

Schema-Based Instruction Implemented Under Routine Conditions

2019 ◽  
Author(s):  
Corey Peltier ◽  
Mindy E Lingo ◽  
Faye Autry-Schreffler ◽  
Malarie Deardorff ◽  
Leslie Mathews ◽  
...  
Keyword(s):  
Problem Solving ◽  
Word Problems ◽  
Mathematical Problem ◽  
Functional Relation ◽  
Probe Design ◽  
Resource Room ◽  
Group Settings ◽  
Intervention Protocol ◽  
Prior Literature ◽  
Based Instruction

Students identified with a specific learning disability (SLD) experience difficulty with mathematical problem solving. One specific intervention identified as a promising practice for students with a SLD is schema-based instruction (SBI). The current projects aimed to tests the efficacy of SBI under routine conditions. This extends prior literature by (a) using a teacher as the implementer, (b) allowing flexibility in the intervention protocol, (c) condensing the duration of intervention sessions, and (d) providing instruction in small group settings. In addition, we examined student problem solving performance on word problems requiring two-steps and combined schema structures. We used a multiple-probe design across three groups of fifth-grade participants (n = 7) receiving supplemental instruction in a resource room setting. Results indicated a functional relation between SBI and problem-solving performance for all students on simple structure word problems, with the magnitude of effects varying across cases. The NAP, Tau, and BC-SMD effect sizes were used to quantify effects. Implications were discussed in regard to systematic replication and conditions that may impact fidelity.

Shifting Roles in Continuous Advising Sessions

Relay Journal ◽  
2019 ◽  
pp. 69-72
Author(s):  
Huw Davies ◽  
Robert Stevenson ◽  
Isra Wongsarnpigoon
Keyword(s):  
Learning Process ◽  
Transformational Learning ◽  
Learning Trajectory ◽  
Learner Readiness ◽  
Linguistic Support ◽  
Reflective Dialogue ◽  
Open Mind ◽  
To Receive

It is common for learning advisors to receive a request such as conversation practice or simple linguistic support in our institution simply because learners find them accessible and friendly. Although this may not be the usual role of a learning advisor, it can be the beginning of a long-lasting reflective dialogue. Learning advisors are aware that the learners’ initial interest is not necessarily an opportunity for reflection on their learning process. Nevertheless, they also acknowledge the fact that learner readiness for reflection varies depending on the learner. Thus, while advisors appear to be “conversation partners” at first, they endeavor to create reflective dialogues by incorporating advising strategies in each session. As the learning trajectory that the learner follows is not always straightforward, keeping an open mind and engaging in each advising session is crucial. The following stories depict the importance of openness to learners’ needs and maintaining continuous advising sessions in order to generate transformational learning.

scholarly journals Arithmetic Word Problems Revisited: Cognitive Processes and Academic Performance in Secondary School

2021 ◽  
Vol 11 (4) ◽  
pp. 155
Author(s):  
Gonzalo Duque de Blas ◽  
Isabel Gómez-Veiga ◽  
Juan A. García-Madruga
Keyword(s):  
Academic Performance ◽  
Word Problems ◽  
Spatial Reasoning ◽  
Deductive Reasoning ◽  
Executive Processes ◽  
Mathematical Operation ◽  
Visual Spatial ◽  
And Mathematics ◽  
The One ◽  
Memory Resources

Solving arithmetic word problems is a complex task that requires individuals to activate their working memory resources, as well as the correct performance of the underlying executive processes involved in order to inhibit semantic biases or superficial responses caused by the problem’s statement. This paper describes a study carried out with 135 students of Secondary Obligatory Education, each of whom solved 5 verbal arithmetic problems: 2 consistent problems, whose mathematical operation (add/subtract) and the verbal statement of the problem coincide, and 3 inconsistent problems, whose required operation is the inverse of the one suggested by the verbal term(s). Measures of reading comprehension, visual–spatial reasoning and deductive reasoning were also obtained. The results show the relationship between arithmetic problems and cognitive measures, as well as the ability of these problems to predict academic performance. Regression analyses confirmed that arithmetic word problems were the only measure with significant power of association with academic achievement in both History/Geography (β = 0.25) and Mathematics (β = 0.23).

scholarly journals Students’ suspension of sense making in problem solving

ZDM ◽  
2021 ◽  
Author(s):  
Gemma Carotenuto ◽  
Pietro Di Martino ◽  
Marta Lemmi
Keyword(s):  
Problem Solving ◽  
Qualitative Study ◽  
Word Problem ◽  
Word Problems ◽  
Mathematical Problem ◽  
Critical Issue ◽  
Mathematical Problem Solving ◽  
Sense Making ◽  
Mathematical Problems

AbstractResearch on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the presence of words and expressions having many and sometimes opposite meanings. Significant examples are the terms ‘realistic’ and ‘modeling’ associated with word problems in school. Understanding how these terms are used is important in research, because this issue relates to the design of several studies and to the interpretation of a large number of phenomena, such as the well-known phenomenon of students’ suspension of sense making when they solve mathematical problems. In order to deepen our understanding of this phenomenon, we describe a large empirical and qualitative study focused on the effects of variations in the presentation (text, picture, format) of word problems on students’ approaches to these problems. The results of our study show that the phenomenon of suspension of sense making is more precisely a phenomenon of activation of alternative kinds of sense making: the different kinds of active sense making appear to be strongly affected by the presentation of the word problem.

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