Constructivist Approach

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


Divergent (OPEN-ENDED) Questions

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

Convergent (CLOSED) Questions

  • 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)

The 3 stages teachers should use when introducing a new topic
Concrete Stage

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


ex. using counters to model an addition problem

Representational Stage

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



Abstract Stage

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

Problem-Solving Approach

  • 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

Draw a Picture

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?

Problem Solving Strategies

  • 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…

Working Backwards

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?

Guess, Check, and Revise

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?

Authentic Assessments

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



Student Portfolios

Student-Teacher Interviews

Summative Assessment

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

Formative Assessment

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

A quiz given after a lesson has been presented is what type of assessment
Advantages of using a rubric

  • 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

concept of ratio

Manipulatives such as:





learning disabilities
teaching math concepts from the concrete to the representational to the abstract will help a diverse group of students to include those with…
place value

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