Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 12 - Building Strategies for Whole-Number Computation (Development…
Chapter 12 - Building Strategies for Whole-Number Computation
A Move to Computational Fluency
Add/subtract that build on composing and composing numbers contributes to children's overall number sense
Easier and faster than standard algorithms and often done mentally
"Number talks" let children have opportunities to engage in solving and discussing alternative strategies to solve computation problems
Connecting Addition and Subtraction to Place Value
Addition and subtraction are good context for learning place-value concepts
If children only understand computation as digit-by-digit, they make many more errors and are often unable to make reason of answer
Children develop place-value understanding as a result of their own methods of add and subtract multidigit numbers
Three Types of Computational Strategies
Direct Modeling
Use of manipulatives, drawings,or fingers along with counting to directly represent numbers involved and meaning of operation
Children who consistently count by ones in addition most likely have not developed base-ten grouping concepts
When children have constructed of ten as a unit, they begin to use this idea to move from \direct modeling to invented
Invented
Any strategy other than standard algorithm, that doesn’t involve the use of physical materials or counting by ones
At times, invented become mental methods after ideas have been explored, used, discussed and understood
Studies show children in and out of school can construct methods of add and subtract multi-digit numbers without explicit instruction
Standard
Standard should be making sense of the prodcedure as a process and not learning a memorized series of steps
Standard may result in thinking there is only one best approach and one “right” algorithm but that is not true
Standard algorithms must be understood, delaying standard can help learn other algorithms, and cultural differences can influence on what algorithms work best
Development of Invented Strategies
Creating a Supportive Environment
Invented strategies are developed from a strong understanding of numbers
Development of place-value concepts begins to prepare children for the challenges of inventing computational strategies
Avoid immediately identifying the right answer, expect and encourage dicussions, promote curiosity and openness and new ideas
Models to Support Invented Strategies
Both the word split and the use of visual diagram help children develop strategies
Empty number line and shortcut strategy are two different was to diagram and develop invented strategies
The numbers involved in a problem as well as the type of problem will influence the strategies children use
Development of Invented Strategies for Addition and Subtraction
Adding and Subtracting Single-Digit Numbers
Goal is to extend children's knowledge of basic facts and the ten-structure of number system so counting isn't required
Extends children's thinking of making a 10 strategy & down under 10 strategy
Encourage students to solve problems mentally then explain their thinking
Adding Two-Digit Numbers
Fluency must be built through years of exploration using concrete models and strategies
Have children think about adjusting numbers by using 10 as an anchor
Subtraction as Think Addition
Successful with children with disabilites
Use join with change or missing-part problems
Story problems are most successful in demonstrating how these problems work
Take-Away subtraction
Considerably more difficult to do mentally imagining numbers
For many problems the think addition is easier than take away