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


Divergent (OPENENDED) 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)


ConcreteRepresentationalAbstract 

The 3 stages teachers should use when introducing a new topic 


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 realworld 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?


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…



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 bitesized 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
StudentTeacher 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



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



Manipulatives such as:
dominoes
geoboards
money
DO NOT TEACH THE…



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


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

