Framing a robust understanding of proportional reasoning for teachers

Weiland, Travis; Orrill, Chandra Hawley; Nagar, Gili Gal; Brown, Rachael Eriksen; Burke, J. P.

doi:10.1007/s10857-019-09453-0

Cited by 31 publications

(19 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Many previous studies (Stafford et al, 2015;Toluk-Ucar and Bozkus, 2018;Arican, 2019a;Memiş and Yanik, 2019;Weiland et al, 2020;Ozturk et al, 2021) have indicated that there are many and varied difficulties facing teachers and students in the field of proportional reasoning and related topics, and there are errors made by teachers and students in this field, and the most common errors that are made by students and teachers are as follows: Failure to distinguish between proportional and non-proportional situations, use of the additive comparison in proportional situations, and use of the multiplicative comparison in non-proportional situations. Some of these studies (Ojose, 2015;Glover, 2016;Yeong and Martinez, 2016;Andini and Jupri, 2017;Soyak and Isiksal, 2017;Nasir, 2018;Çalışıcı, 2018;Çelen, 2018) also showed that students and teachers have weaknesses in proportional reasoning due to how subjects related to proportional reasoning are taught, how topics related to proportional reasoning are presented in mathematics textbooks, and non-variety in proportional problems in real-life contexts.…”

Section: Review Of Literaturementioning

confidence: 94%

The Effect of Error Analysis-Based Learning on Proportional Reasoning Ability of Seventh-Grade Students

Khasawneh

Al‐Barakat

Almahmoud³

2022

Front. Educ.

View full text Add to dashboard Cite

This study investigated the effect of mathematical error analysis-based learning on proportional reasoning ability of seventh-grade students. To achieve the purpose of the study, a proportion unit for the seventh-grade students in Jordan was designed according to the error analysis-based learning. A sample of 45 seventh-grade students participated in the study and were randomly assigned into the following two groups: Experimental group and control group. The data were collected through the following two instruments: A proportional reasoning test and an interview, after ensuring their reliability and validity. The results of the study revealed that the error analysis-based learning led to a significant improvement in proportional reasoning among the experimental group and contributed to providing students with positive experiences in learning mathematics. In light of these results, a set of recommendations for educational researchers, mathematics curriculum designers, and mathematics teachers were presented.

show abstract

Section: Review Of Literaturementioning

confidence: 94%

The Effect of Error Analysis-Based Learning on Proportional Reasoning Ability of Seventh-Grade Students

Khasawneh

Al‐Barakat

Almahmoud³

2022

Front. Educ.

View full text Add to dashboard Cite

show abstract

“…According to Weiland et al [40] the following requirements in Table 2 should be achieved in order to have a robust understanding of proportional reasoning for teaching.…”

Section: Participants and General Methodologymentioning

confidence: 99%

Understanding of Inverse Proportional Reasoning in Pre-Service Teachers

et al. 2020

View full text Add to dashboard Cite

From an early age, understanding proportional reasoning is a fundamental pillar in mathematics education, and therefore, teachers should have a thorough knowledge of it. Despite its significance, there are few studies that analyse the difficulties that student teachers have in understanding proportionality, and even less so inverse proportionality. We emphasised inverse missing-value problems by analysing them according to the type of unknown and the representation used. We checked which strategies they use to solve them and related them to other generic problems of proportional reasoning. For such purposes, we used a combined quantitative and qualitative empirical study applied to how pre-service teachers solve fifteen problems. The results show that the representations used in the statements aid their understanding and help solve the problems. Similarly, it is shown here that certain problem-solving strategies complicate proportional reasoning in pre-service teachers.

show abstract

“…Several studies have demonstrated that PSTs have problems with understanding proportional reasoning (Arican, 2019;Ben-Chaim et al, 2007;Glassmeyer et al, 2021;Hines & McMahon, 2005;Izsak & Jacobson, 2017;Livy & Herbert, 2013;Weiland et al, 2021). For example, Izsak and Jacobson (2017) reported that PSTs have difficulty with distinguishing proportional relationships from other relationships between two co-varying quantities, and not surprisingly, elementary students have been shown to have similar struggles (Ucar & Bozkus, 2018;Vershaffel et al, 1997).…”

Section: Psts' Proportional Reasoningmentioning

confidence: 99%

“…Proportional reasoning, cited in the common core as one of the eleven mathematical domains that span mathematics from elementary to high school (National Governors Association Center for Best Practices, 2010), has also been widely investigated as a key type of reasoning with which both students and teachers in K-12 mathematics classrooms struggle (Beckmann & Izsak, 2015;Byerley & Thompson, 2017;Weiland et al, 2021). According to Lamon (2007), proportional reasoning is defined as "detecting, expressing, analyzing, explaining, and providing evidence in support of assertions about proportional relationships between two co-varying quantities" (p. 647).…”

Section: Introductionmentioning

confidence: 99%

Incoherencies in elementary pre-service teachers’ understanding of calculations in proportional tasks

Lee¹,

Joshua²

2022

INT ELECT J MATH ED

View full text Add to dashboard Cite

In this study we investigated pre-service teachers' (PSTs) proportional reasoning and how they interpret their calculations in proportional tasks. We administered a written questionnaire to 199 PSTs and used an inductive content analysis approach for data analysis. We found that one item, in which PSTs were asked to interpret the meaning of the results of their calculations, had unusually low coherency, and applying open coding to the responses revealed several common errors. We argue these common errors cannot be dismissed as simple unit or rounding mistakes but rather reflect problems in how respondents think about quantities, story problems, and the nature of mathematics itself. We end with suggestions on how to address these problems.

show abstract

Framing a robust understanding of proportional reasoning for teachers

Cited by 31 publications

References 23 publications

The Effect of Error Analysis-Based Learning on Proportional Reasoning Ability of Seventh-Grade Students

The Effect of Error Analysis-Based Learning on Proportional Reasoning Ability of Seventh-Grade Students

Understanding of Inverse Proportional Reasoning in Pre-Service Teachers

Incoherencies in elementary pre-service teachers’ understanding of calculations in proportional tasks

Contact Info

Product

Resources

About