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Download full textWadham, Bridget; Pearce, Emily; Hunter, Jodie – Mathematics Education Research Group of Australasia, 2023
In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…
Descriptors: Algebra, Mathematics Instruction, Multiplication, Learning Processes
Aparicio Landa, Eddie; Sosa Moguel, Landy; Cabañas-Sánchez, Guadalupe – International Journal of Education in Mathematics, Science and Technology, 2021
This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to…
Descriptors: Mathematical Concepts, Mathematics Instruction, Geometry, Algebra
Tillema, Erik; Gatza, Andrew – North American Chapter of the International Group for the Psychology of Mathematics Education, 2015
The study reported on in this paper is an interview study conducted with 20 7th and 8th grade students whose purpose was to understand the generalizations they could make about non-linear meanings of multiplication (NLMM) and non-linear growth (NLG) in the context of solving combinatorics problems. The paper identifies productive challenges for…
Descriptors: Middle School Students, Secondary School Mathematics, Generalization, Number Concepts
Direct linkStrickland, Tricia K.; Maccini, Paula – Remedial and Special Education, 2013
We examined the effects of the Concrete-Representational-Abstract Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the…
Descriptors: Learning Disabilities, Multiplication, Mathematics Skills, Secondary School Mathematics
Hackenberg, Amy J.; Lee, Mi Yeon – North American Chapter of the International Group for the Psychology of Mathematics Education, 2012
To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of 3 different multiplicative concepts participated. This paper reports on the 6 students with the most basic multiplicative…
Descriptors: Middle School Students, Mathematics Instruction, Logical Thinking, Fractions
Gierdien, Faaiz – International Journal of Mathematical Education in Science and Technology, 2009
This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…
Descriptors: Arithmetic, Multiplication, Mathematics Instruction, Mathematical Concepts
Peer reviewedOlson, Alton T. – Mathematics Teacher, 1974
Descriptors: Algebra, Algorithms, Generalization, Induction
