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Expanding theCBAL™ Mathematics Assessments to Elementary Grades: The Development of a Competency Model and a Rational Number Learning Progression

Meirav Arieli-Attali, Gabrielle Cayton-Hodges
2014 ETS Research Report Series  
Acknowledgments The authors would like to acknowledge the following staff members who contributed to the work of CBAL elementary mathematics in 2012 that is reflected in this report: • Lastly, we especially  ...  want to thank the students and teachers who participated in our cognitive interviews and in that participation contributed to our project.  ...  We chose rational numbers as this concept is a central topic in elementary school mathematics with implications for future mathematical understanding through algebra and beyond. 3.  ... 
doi:10.1002/ets2.12008 fatcat:3tcs4yljpbbbpdw7xz4vsszsa4

12 Math Rules That Expire in the Middle Grades

Karen S. Karp, Sarah B. Bush, Barbara J. Dougherty
2015 Mathematics Teaching in the Middle School  
, and statistics, while reinforcing critical mathematical practices and habits of mind.  ...  Students who develop financial literacy are equipped to make better financial decisionsabout budgeting, saving, buying on credit, investing, and a host of other topics.  ...  She is a co-author of conceptual assessments for progress monitoring in algebra and curriculum modules for middle school interventions for students who struggle.  ... 
doi:10.5951/mathteacmiddscho.21.4.0208 fatcat:bbxphsdp5bbjjedc7n7dxfryhy

Conceptualizing alternative ways of curricular teaching through technology

Kumar Laxman
2012 i-manager s Journal on School Educational Technology  
This has resulted in growing calls for reforms in traditional ways of algebra instructions to re-conceptualise and invigorate the learning of algebra content in schools.  ...  Traditional methods of teaching algebra encourage students to identify algebraic notations and perform procedural computations without comprehending the underlying relationships between the different modes  ...  by generative design activities in a next-generation classroom networked technology via IT navigator system promotes the learning of algebra in the classroom in more meaningful ways.  ... 
doi:10.26634/jsch.8.1.1915 fatcat:if35cmidsncsffrrfecgs4qvka

Seeing Spots and Developing Multiplicative Sense Making

Gabriel T. Matney, Brooke N. Daugherty
2013 Mathematics Teaching in the Middle School  
Algebraic expressions and equations, in which students write expressions, identify equivalencies, and evaluate multiplicative expressions of realworld problems using algebraic notation (6.EE, pp. 43−44  ...  Vol. 19, No. 3, October 2013 G MATHEMATICS TEACHING IN THE MIDDLE SCHOOL 155  ... 
doi:10.5951/mathteacmiddscho.19.3.0148 fatcat:ujhl2ytkxvblzjjhqhztg3nabu

Survey of the State of the Art [chapter]

Carolyn Kieran, JeongSuk Pang, Deborah Schifter, Swee Fong Ng
2016 ICME-13 Topical Surveys  
and curricula as students progress through elementary and middle school.  ...  When children are able to perform arithmetic operations accurately and with automaticity, they have greater opportunities to perform more complex mathematical tasks (Menon 2010), such as exploring relationships  ... 
doi:10.1007/978-3-319-32258-2_2 fatcat:y2wfi7tb6bdbxmfp43gooh46ae

Using tasks to bring challenge in mathematics classroom

Ioannis Papadopoulos
2020 Journal of Pedagogical Research  
Some challenging tasks in the paper-and-pencil as well as in a digital environment will be presented.  ...  Rich and challenging tasks can be the vehicle to bring mathematical challenge in classroom.  ...  This article is based on my plenary talk at the International Congress of Pedagogical Research ICOPR"2020 held at Duzce University, Turkey, in June, 2020.  ... 
doi:10.33902/jpr.2020063021 fatcat:rdokmhhbtrad3ep7gv4kx7rh7e

Representing equality

Zeina Atrash Leong, Michael S. Horn
2011 Proceedings of the 10th International Conference on Interaction Design and Children - IDC '11  
We also present data from an exploratory study with seven children (ages 9-10 years) in a local elementary summer school classroom.  ...  Whether or not the combination of physical and digital representations provided by our interface helps students apply this relational understanding to equations written using standard algebraic notation  ...  Though many digitally enhanced manipulatives with mathematical focus have been developed, those with a focus in algebra are rare.  ... 
doi:10.1145/1999030.1999054 dblp:conf/acmidc/LeongH11 fatcat:gyfl66iu5vd3lkk6wvba7tymeq

Preservice Elementary Teacher's Thinking about Algebraic Reasoning

Walter F. Castro Gordillo, Juan D. Godino
2014 IEJME-Mathematics Education  
reasoning in primary school curriculum.  ...  This paper reports on the results of a research about the comprehension of elementary algebraic reasoning exhibited by preservice elementary teachers.  ...  Acknowledgements This research work has been carried out partially in the frame of the project EDU2012-31869. Ministerio de Economía y Competitividad (MINECO, España).  ... 
doi:10.29333/iejme/287 fatcat:dftvbhy5brblhlk5ksnwil3nei

The introduction of real numbers in secondary education: an institutional analysis of textbooks

Alejandro S. González-Martín, Victor Giraldo, Alexandre M. Souto
2013 Research in Mathematics Education  
In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, as they are proposed to be taught, from a sample of Brazilian textbooks used in public schools and approved  ...  It seems that textbooks used in secondary teaching institutions develop mathematical organisations which focus on the practical block.  ...  More recently, Stylianides' (2009) study analysed a middle school mathematics textbook series to see how reasoning-andproving tasks are promoted in the algebra, number theory, and geometry units.However  ... 
doi:10.1080/14794802.2013.803778 fatcat:tdpoljbguvdrbocqgfrnstdvzy

The Future of Embodied Design for Mathematics Teaching and Learning

Dor Abrahamson, Mitchell J. Nathan, Caro Williams-Pierce, Candace Walkington, Erin R. Ottmar, Hortensia Soto, Martha W. Alibali
2020 Frontiers in Education  
We-a cohort of cognitive scientists and design-based researchers of embodied mathematics-survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning  ...  The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology.  ...  These designs were each evaluated empirically with several dozen middle-school students, who participated individually or in pairs in task-based semi-structured clinical interviews.  ... 
doi:10.3389/feduc.2020.00147 fatcat:dlthbtsmkvdwfd5gqzlni4gaoe

An Investigation Into 3-, 4-, and 5-Year-Old Children's Nonsymbolic Magnitude Comparison Ability According to Ratio Limit and Task Condition

Woomi Cho, Soon-Hyung Yi
2017 Adonghakoeji  
notation system.  ...  The fact that the algebra system can be °run on its own," so to speak, is surely a factor in favor of its efficiency.  ...  Then they decomposed 4 x 9 I: to 2 x 9 plus 2 a 9. Then they set up a missing addend problem, 36 * 69, it-hich they solved by a combination of estimation and correelon.  ... 
doi:10.5723/kjcs.2017.38.1.117 fatcat:btnu74n4zrfozatulb5i2qlb7m

TME Volume 11, Number 2

2014 The Mathematics Enthusiast  
The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning.  ...  Articles appearing in the journal address issues related to mathematical thinking, teaching and learning at all levels.  ...  -We also included prospective middle school teachers because some certification programs focus on K-8, and not all countries follow the same school system.  ... 
doi:10.54870/1551-3440.1310 fatcat:wcijcfwu2jes7hzlmieok4dpgu

Why is learning fraction and decimal arithmetic so difficult?

Hugues Lortie-Forgues, Jing Tian, Robert S. Siegler
2015 Developmental Review  
A B S T R A C T Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions.  ...  Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades.  ...  Consistent with this hypothesis, knowledge of fraction magnitudes in middle school predicts later algebra learning (Bailey et al., 2012; Booth & Newton, 2012; Booth et al., 2014) .  ... 
doi:10.1016/j.dr.2015.07.008 fatcat:66hojhdtdfg5fd5pol4rqwueku

Word problems: a review of linguistic and numerical factors contributing to their difficulty

Gabriella Daroczy, Magdalena Wolska, Walt Detmar Meurers, Hans-Christoph Nuerk
2015 Frontiers in Psychology  
In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly  ...  We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group  ...  Acknowledgments This research was funded by the LEAD Graduate School [GSC1028], a project of the Excellence Initiative of the German federal and state governments.  ... 
doi:10.3389/fpsyg.2015.00348 pmid:25883575 pmcid:PMC4381502 fatcat:v6rix63g65afviaa3bcotc57oa

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners

Sarah R. Powell, Lynn S. Fuchs, Paul T. Cirino, Douglas Fuchs, Donald L. Compton, Paul C. Changas
2015 Exceptional children  
The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2 nd -grade students at risk for mathematics difficulty.  ...  Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group  ...  in late elementary, middle, and high school.  ... 
doi:10.1177/0014402914563702 pmid:26097244 pmcid:PMC4470425 fatcat:owbiywahmjdwxoaq6d25bbfrla
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