scholarly journals Manipulatives and Multiplicative Thinking

2020 ◽  
Vol 5 (1) ◽  
pp. 04
Author(s):  
Chris Hurst ◽  
Chris Linsell
Keyword(s):  
Multiplicative Thinking

Developing Multiplicative Thinking from Additive Reasoning

2013 ◽  
Vol 20 (2) ◽  
pp. 102-109
Author(s):  
Jennifer M. Tobias ◽  
Janet B. Andreasen
Keyword(s):  
Equivalent Fractions ◽  
Additive Reasoning ◽  
Multiplicative Thinking

Using the context of restaurants and ratios to find equivalent fractions can push students' strategies forward.

scholarly journals Language-responsive support for multiplicative thinking as unitizing: results of an intervention study in the second grade

ZDM ◽  
2020 ◽  
Author(s):  
Daniela Götze ◽  
Annica Baiker
Keyword(s):  
Meaning Making ◽  
Second Grade ◽  
Control Group ◽  
Primary School Teachers ◽  
Multiplicative Thinking ◽  
Group A ◽  
Abstract Level ◽  
Core Idea ◽  
And Control

AbstractMultiplicative thinking involves the ability to coordinate bundled units on a more abstract level than additive thinking and implies the identification of the different meanings of the multiplier and the multiplicand. The transition from additive to multiplicative thinking, however, constitutes an obstacle for many children. Specific formulations that are typically used in classroom discourse for talking about multiplicative tasks and situations (e.g., ‘3 times 4’ or ‘3 lots of 4’) might inhibit meaning-making processes because they do not address the idea of unitizing. A language-responsive introduction to multiplication that addresses the core idea of unitizing and that uses phrases such as ‘3 times 4 means you have 3 fours’ may help to overcome these problems. In the study presented in this paper, three second grade primary school teachers joined a teacher program to introduce multiplication in their classes (n = 66) by addressing meaning-making phrases. Another 58 second graders taught by teachers without this teacher program served as the control group. A specially developed multiplication test gave insight into the children’s understanding of multiplication as unitizing immediately after the intervention (posttest) and nearly three months later (follow-up test). We found significant differences between the intervention and control groups in the multiplication posttest. These differences could be underlined in the follow-up test. Our results indicate that a language-responsive teaching intervention that focuses on meaning-making processes can lead to long-term insights and help to develop multiplicative thinking as unitizing.

Connecting Research and Practice – The Case of Multiplicative Thinking

2019 ◽  
pp. 535-540
Author(s):  
Dianne Siemon
Keyword(s):  
Formative Assessment ◽  
School Mathematics ◽  
Assessment Tools ◽  
Evidence Based ◽  
Middle Years ◽  
Research And Practice ◽  
Whole Numbers ◽  
Middle Years Of Schooling ◽  
Multiplicative Thinking ◽  
Division Problems

There is very little of any substance that can be achieved in school mathematics, and beyond without the capacity to recognise, represent and reason about relationships between quantities, that is, to think multiplicatively. However, research has consistently found that while most students in the middle years of schooling (i.e., Years 5 to 9) are able to solve simple multiplication and division problems involving small whole numbers, they rely on additive strategies to solve more complex problems involving larger numbers, fractions, decimals, and/or proportion. This paper describes how this situation can be addressed through the use of evidence-based formative assessment tools and teaching advice specifically designed to support the development of multiplicative thinking.

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