**Linkages**- Teaching from What is Known to What is New

When introducing new concepts, always take two or three steps back to move three or four steps forward. That means finding the basic conceptual foundation that will support what you need to teach.

Examples include

It is critical that upper elementary and secondary teachers comprehend the concepts and language used to teach basic concepts so that they can take those "two steps back" in order to link new concepts to prior learning. Algebra teachers must totally comprehend how to talk about fraction operations at a basic level and not simply tell their students "how" to get an answer. Students will develop the ability to reason mathematically only if we are all on the same page conceptually.

CONCEPTS RULE! Procedures can get lost in the shuffle.

Examples include

- Reviewing place value before teaching fractions: The unit is "the one." It is the one from which many are made or fractions are cut. Use a place value mat that includes "fractions of one."
- Reviewing fractions as they relate to place value before teaching decimals: Provide a link between fraction concepts and the unique properties of decimal numbers.
- Reviewing multiplication concepts before introducing exponents
- Reviewing multiplication as "making many" of the same quantity and division as "taking apart" by groups of the same quantity
- Review the two meanings of division before asking students to sort word problems: Am I making groups of a specific quantity or making a quantity of groups to see how many would be in each group?
- Review regrouping with whole numbers before teaching regrouping from the whole to the part in fraction operations.

It is critical that upper elementary and secondary teachers comprehend the concepts and language used to teach basic concepts so that they can take those "two steps back" in order to link new concepts to prior learning. Algebra teachers must totally comprehend how to talk about fraction operations at a basic level and not simply tell their students "how" to get an answer. Students will develop the ability to reason mathematically only if we are all on the same page conceptually.

CONCEPTS RULE! Procedures can get lost in the shuffle.