One-step and multi-step linear equations: a content analysis of five textbook series

Huntley, Mary Ann; Terrell, Maria Shea

doi:10.1007/s11858-014-0627-6

Cited by 23 publications

(14 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similarly, early algebra has been described as a "shift from thinking about relations among particular numbers and measures towards thinking about relations among sets of numbers and measures, from computing numerical answers to describing and representing relations among variables" (Carraher, Schliemann, & Schwartz, 2007, p. 266). Solving linear equations as a basic skill (Ballheim, 1999) is a substantial part of the middle school mathematics program (Huntley & Terrell, 2014). However, many students do not achieve mastery of this basic skill and experience difficulties in learning the concepts and skills related to solving equations (e.g., Kieran, 2007).…”

Section: Introductionmentioning

confidence: 99%

The balance model for teaching linear equations: a systematic literature review

2019

View full text Add to dashboard Cite

This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report why such a model is used, what types of models are used, and when they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a comprehensive overview of described rationales for using the balance model, its appearances, situations in which it was used, and the gained learning outcomes. Some trends appeared about how rationales, appearances, situations, and learning outcomes are related. However, a clear pattern could not be identified. Our study shows that this seemingly simple model actually is a rather complex didactic tool of which in-depth knowledge is lacking. Further systematic research is needed for making informed instructional decisions on when and how balance models can be used effectively for teaching linear equation solving.

show abstract

Section: Introductionmentioning

confidence: 99%

The balance model for teaching linear equations: a systematic literature review

2019

View full text Add to dashboard Cite

show abstract

“…Other frequency analysis studies have gone a step further by employing statistical tests to determine the significance of any differences (Löwenhielm et al, 2017). Others, concerned that frequencies alone offer too limited a narrative, have examined the first position of particular tasks in the sequence of all tasks (Fujita, 2001) or the percentage of all tasks before such an occurrence (Alajmi, 2012), while others have presented each task of interest as a dot in the timeline of all tasks (Huntley & Terrell, 2014). Still others have supplemented frequencies with qualitative descriptions of tasks (Barcelos Amaral & Hollebrands, 2017).…”

Section: Methodsmentioning

confidence: 99%

“…Still others have supplemented frequencies with qualitative descriptions of tasks (Barcelos Amaral & Hollebrands, 2017). All these approaches allow for straightforward and meaningful comparisons and, while Huntley and Terrell's (2014) approach offers an indication of where tasks occur in the overall structure of a textbook, none show how children's learning is structured on a day-to-day, week-to-week or month-to-month basis. In this paper, alongside conventional frequency analyses and their associated statistical significance, we demonstrate how moving averages as a hitherto unconsidered approach to the analysis of textbooks offer important insights with respect to the temporal location and emphases of different forms of mathematical tasks.…”

Section: Methodsmentioning

confidence: 99%

Opportunities to learn foundational number sense in three Swedish year one textbooks: implications for the importation of overseas-authored materials

Sayers

Petersson

Rosenqvist

et al. 2019

International Journal of Mathematical Education in Science and

View full text Add to dashboard Cite

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded against the eight categories of foundational number sense, which are the number-related competences literature has shown to be essential for the later mathematical success of year one learners. Two analyses were undertaken; the first was a frequency analysis of the tasks coded for a particular category, the second was a time-series analysis highlighting the temporal location of such opportunities. The frequency analyses identified statistically significant differences with respect to children's opportunities to acquire foundational number sense. Additionally, the time series showed substantial differences in the ways in which such tasks were located in the structure of the textbooks. Such differences, we argue, offer substantial didactical challenges to teachers trying to adapt their practices to the expectations of such imports.

show abstract

“…They consider how design differences in the materials may explain achievement differences observed during student testing. Huntley and Terrell (2014) conducted a detailed analysis of algebra textbooks or units in integrated textbooks to consider design issues related to the topics of one-step and multi-step linear equations. They consider the sequence of introduction of the topics, cognitive level in terms of performance expectation, and use of other resources such as manipulatives or technology to facilitate learning.…”

Section: Structure Of This Zdm Issuementioning

confidence: 99%

Researching the enacted mathematics curriculum: learning from various perspectives on enactment

Thompson

Huntley

2014

ZDM Mathematics Education

Self Cite

View full text Add to dashboard Cite

affiliated with the Trends in International Mathematics and Science Study (TIMSS), "Perhaps only students and teachers themselves are a more ubiquitous element of schooling than textbooks. … They represent school disciplines to students. They translate a country's curriculum policies into such representations" (Valverde et al. 2002, p. 1). Given the central role of textbooks in shaping and facilitating education, it seems only natural that educators are interested in researching various aspects of textbooks and their use. Indeed, as noted by Fan (2013), research about school textbooks has increased internationally in the last few decades and represents an important area for scientific research. This journal, itself, has recognized the importance of textbook research, with an issue on this topic as recently as volume 45, issue 5, in Fall 2013. In Fall 2010, a conference on researching the enacted mathematics curriculum that was funded by the US National Science Foundation was held in the in Tampa, FL (US). This conference brought together veteran curriculum scholars, relatively new researchers, and doctoral students to begin discussing a conceptual model for researching curriculum enactment. That conference led to a book, Enacted Mathematics Curriculum: A Conceptual Framework and Research Needs (Thompson and Usiskin 2014), to share the findings and discussions of the conference with a larger audience. But we believed there was still more to share. Although the book expanded on the work of the conference, many conference participants had research results related to curriculum enactment that needed to be shared. Hence, this issue of ZDM is one means of sharing that research with a wide international audience. As previously noted, interest in textbook research and enactment of textbook curricula has been expanding throughout the world. In addition to the issue of ZDM in 2013, an international conference on mathematics textbook Abstract This issue of ZDM focuses on research related to the enacted curriculum from various perspectives within the context of the US educational system. In this editorial, we describe the broad view of curriculum enactment taken in this issue, highlighting that we mean more than just how instruction plays out within a classroom. For instance, enactment can occur at a national level as educational goals are enacted into a set of national objectives or standards. Enactment can occur as goals or standards are embedded into written curriculum materials or textbooks, both in terms of teacher guides and materials for students. Enactment can occur as teachers make decisions about how to use their written curriculum materials. Finally, enactment can occur as teachers and students engage and interact with written materials during classroom instruction. We elaborate briefly on these views and then outline the structure of this ZDM issue.

show abstract

One-step and multi-step linear equations: a content analysis of five textbook series

Cited by 23 publications

References 4 publications

The balance model for teaching linear equations: a systematic literature review

The balance model for teaching linear equations: a systematic literature review

Opportunities to learn foundational number sense in three Swedish year one textbooks: implications for the importation of overseas-authored materials

Researching the enacted mathematics curriculum: learning from various perspectives on enactment

Contact Info

Product

Resources

About