• Students construct their own knowledge and/or meaning
• active experimentation and interaction with peers, teachers, materials
• discovery learning is encourage 

• do not have one specific answer; thinking outside the box
• allows for creative thinking
• should be encouaged by all students
• many possible answers

• asking for a specific response
• only has 1 answer
• these type of question can stiffle a child's creativity

ex.  what unit do we use to measure a bag of potatoes?  ONLY 1 ANSWER (Pounds)

During this stage, the teacher introduces and models the concept by using tools or manipulatives

ex. using counters to model an addition problem

During this stage, the teacher transforms manipulatives into a symbolic form by drawing pictures or making tally marks

During this stage, the teacher models how to complete the task using only numbers and math symbols

ex. changing the tally marks into numbers like 3+5=8

• the primary goal of math
• known as a process and not a topic
• introduced through real-world situations
• allows student to explain and discuss ways fo arriving at their solution

Julie is 10 meters ahead fo Mary. Shon is 5 meters behind Julie.  Mary is 12 meters behind Lisa.  In what order ar ethe runner from first to last?

What problem solving strategy is most effective for solving this?

• working bckwards
• find a pattern
• act it out
• draw a picture
• guess, test, revise
• make a table
• try a simpler problem
• make a model
• guess & check

are all...

Alan took $20.00 to the grocery store.  He bought a chicken for $3.09, celery for $.79, milk for $2.02, and some bread.  He received $12.42 in change.  How much did the bread cost?

What strategy would be used to solve this problem?

You have 30 bite-sized snickers to share with your sister. You want to keep 4 more than you give her.  How many should she get?

What problem solving strategy should you use?

Used to assess students's ability to apply what has been learned

Includes:

Student Portfolios

Student-Teacher Interviews

These assessments are given at the end of a unit, end of a chapter exam, or end of year

Does not help the teacher in modifying instruction or reteaching

This type of assessment is part of the instructional process.

Provides information to the teacher during student learning so that instruction can be adjustedor arranged for reteaching

• allow assessments to be more objective and consistent
• show students clearly how work will be evaluated
• provides useful feedback to teacher regarding effectiveness of instruction

Manipulatives such as:

-dominoes

-geoboards

-money

DO NOT TEACH THE...

determines the value of a digit by its position

an example would be a game in which students draw 4 boxes.  they then take turns throwing a dice.  each time the dice is thrown, students write the number shown on the dice in any one of the 4 boxes; the game continues until all 4 boxes have numbers.  students compare number and the one with the largest wins