IN-BETWEENNESS
IN-BETWEENNESS
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What does it mean?
What does it mean?
In-betweenness defines an interval in which a value can exist rather than a single answer. In general, it offers a range of values between some lower and upper limit.
Why is In-Betweenness in the Equality & Inequality family of seeds?
Why is In-Betweenness in the Equality & Inequality family of seeds?
In-betweenness relates to both equality and inequality: the concept of being “in between” defines a range inside which a variable amount is equal to some value, and the range itself is based on numbers the variable amount is not equal to: one less, one greater.
How does this connect to Algebra?
How does this connect to Algebra?
The idea of in-betweenness can eventually be formally expressed as the Intermediate Value Theorem (Walkoe & Levin, 2020, p.30). It might also be called upon when thinking about compound inequalities or, much later, the Squeeze Theorem regarding limits of functions that fall “in between” two other functions.
What might children say?
What might children say?
Children may describe a value or range falling in between two limits as "in between," or "in the middle" of the two endpoints. They may describe the upper and lower limit as "narrowing down" the range of possible values.
What might children do?
What might children do?
Children might make hand gestures showing a range (with each hand as a limit or endpoint); this might serve as a physical representation for numbers or objects "in between" the hands vs. outside.
Later, guess-and-check methods might be used to define "too high" and "too low" limits to narrow down an answer.
In the story of Goldilocks and the Three Bears, Goldilocks discovers porridge that is too hot, too cold, and then just right. (Walkoe & Levin, 2020, p. 29)
When parents measure growth on a door frame, if they happen to skip a month, they can make a solid guess about the child’s height during that particular month (Walkoe & Levin, 2020, p. 30).
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