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Ngu, Bing Hiong; Phan, Huy P. – Educational Psychology Review, 2016
The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…
Descriptors: Equations (Mathematics), Cognitive Processes, Difficulty Level, Mathematics Instruction
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Watt, Sarah J.; Watkins, Jessie R.; Abbitt, Jason – Journal of Learning Disabilities, 2016
This review investigates effective interventions for teaching algebra to students with learning disabilities and evaluates the complexity and alignment of skills with the Common Core State Standards in math. The review includes the results of 10 experimental and 5 single-subject designs (N = 15) producing a moderate overall effect size (g = 0.48).…
Descriptors: Algebra, Learning Disabilities, Mathematics Instruction, Intervention
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Blanton, Maria; Brizuela, Bárbara M.; Gardiner, Angela Murphy; Sawrey, Katie; Newman-Owens, Ashley – Journal for Research in Mathematics Education, 2015
The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional…
Descriptors: Young Children, Elementary School Students, Grade 1, Mathematics Instruction
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Sztajn, Paola; Wilson, P. Holt; Edgington, Cyndi; Confrey, Jere – North American Chapter of the International Group for the Psychology of Mathematics Education, 2011
As learning trajectories gain traction in mathematics education, we seek to understand the ways in which teachers may use them in interactions with students. This paper reports on one group of elementary teachers' use of their emerging knowledge of a learning trajectory to examine key pedagogical practices. Findings suggest that a learning…
Descriptors: Mathematics Instruction, Teaching Methods, Elementary School Teachers, Learning Processes
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Mamona-Downs, Joanna – International Journal of Mathematical Education in Science and Technology, 2010
An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that…
Descriptors: Cognitive Processes, Comparative Analysis, Thinking Skills, Calculus
Usnick, Virginia E. – Focus on Learning Problems in Mathematics, 1992
This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…
Descriptors: Addition, Cognitive Development, Cognitive Processes, Computation
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Jitendra, Asha; Xin, Yan Ping – Journal of Special Education, 1997
Summarizes 14 mathematics word-problem-solving intervention studies for elementary and secondary students with disabilities or who were at-risk for math failure. Interventions included representational techniques (diagramming), strategy-training procedures (cognitive and metacognitive), task variations (sequencing and word-problem context), and…
Descriptors: Cognitive Processes, Computer Assisted Instruction, Diagrams, Elementary Secondary Education