teaching

Instructional Scaffolding – Subtraction with Regrouping

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Whether teachers realize it or not, they are continuously scaffolding instruction for their students. The dictionary definition of scaffolding is: a temporary structure on the outside of a building, made usually of wooden planks and metal poles, used by workers while building, repairing, or cleaning the building. This definition applies quite well to its’ educational connotation. Instructional scaffolding is temporary. It allows students to build, repair, and/or polish their understanding of concepts and skills. It is used temporarily to support students as they develop the required knowledge/skill needed to do something independently or progress to the next level of a skill.

Instructional Scaffolding – Addition with Regrouping

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Whether teachers realize it or not, they are continuously scaffolding instruction for their students. The dictionary definition of scaffolding is: a temporary structure on the outside of a building, made usually of wooden planks and metal poles, used by workers while building, repairing, or cleaning the building. This definition applies quite well to its’ educational connotation. Instructional scaffolding is temporary. It allows students to build, repair, and/or polish their understanding of concepts and skills. It is used temporarily to support students as they develop the required knowledge/skill needed to do something independently or progress to the next level of a skill.

Instructional Scaffolding – Constructing Learning

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Whether teachers realize it or not, they are continuously scaffolding instruction for their students. The dictionary definition of scaffolding is: a temporary structure on the outside of a building, made usually of wooden planks and metal poles, used by workers while building, repairing, or cleaning the building. This definition applies quite well to its’ educational connotation. Instructional scaffolding is temporary. It allows students to build, repair, and/or polish their understanding of concepts and skills. It is used temporarily to support students as they develop the required knowledge/skill needed to do something independently or progress to the next level of a skill.

Even and Odd – A Forgotten Concept

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Student in 2nd Grade are expected to determine if a set of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express an even number as the sum of two equal addends (CCSSMath.Content.2.OA.C3). The “even and odd” concept/skills are not explicitly addressed in any other grade level standards beyond 2nd Grade. It is for this reason that the concept of ‘even and odd’ is a ‘forgotten concept’ for many upper elementary students.

No Gimmicks, Just Schema – Addition with Regrouping

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‘Schema’ as described in this article refers to the prior knowledge and life experience a student brings to a novel task which will assist her or him in making connections to the task to build new understanding. Often in math related articles, ‘schema’ refers to ‘schematic’ diagrams or models, for number stories, but in this article ‘schema’ is used as it is in Language Arts – prior knowledge/experience.

The ‘Hybrid Method’ for Addition with Regrouping – The Missing Step

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Upper elementary students learn the standard algorithm for addition at some point during their elementary math instruction. It is generally the most efficient computational method, and it is essential for efficient multiplication computations later on in the curriculum. Teachers often introduce the algorithm conceptually by demonstrating the process with base ten blocks. Next, students solve addition computations pictorially using base ten block notation. Once students have success adding with pictures, teachers naturally transition to having students add with numbers.

The ‘Hybrid Method’ for Subtraction with Regrouping – The Missing Step

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Upper elementary students learn the standard algorithm for subtraction at some point during their elementary math instruction. It is generally the most efficient computational method, and it is essential for efficient division computations later on in the curriculum. Teachers often introduce the algorithm conceptually by demonstrating the process with base ten blocks. Next, students solve subtraction computations pictorially using base ten block notation. Once students have success subtracting with pictures, teachers naturally transition to having students subtract with numbers.

No Gimmicks, Just Schema – Subtraction with Regrouping

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5 ‘Novel’ Steps to Teach Addition with Regrouping – Conceptually

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Teaching the standard algorithm for addition may not be the first method of addition you teach students, but eventually every student should learn how to add using the standard algorithm. Conceptual understanding of the standard algorithms is the type of thinking that is needed to succeed in algebra and advanced mathematics (Wu 2009). The algorithm is based on place value understanding, and it is generally the most efficient addition strategy to use.