Cognitively Guided Instruction: Cognitively Guided Instruction: An introductionAn introduction

Direct Instruction as a Teaching Strategy

Dr. Patty Chastain

Direct InstructionDirect Instruction

Best used when there is factual information that students could not “discover” or develop on their own.

Often starts with a pre-assessment Teacher gives information/lecture Students have some “guided practice”

followed by independent practice Attainment of knowledge assessed to see

change

Cognitively Guided Instruction (CGI)Cognitively Guided Instruction (CGI)

A method of instruction, used especially for teaching arithmetic, based on:– knowledge of students’ current abilities; – usual cognitive development; – levels of difficulties of the tasks assigned

Based on research by Thomas Carpenter and others

Assumes that children learn best when they figure things out for themselves, rather than being shown algorithms (“constructivism”)

CGI basics, continuedCGI basics, continued

Students are presented with problems in context (I.e., story problems)

Story problems vary in difficulty based on how they are worded.

Level of difficulty is determined through research into how young children approach the problem when they can count, but have not memorized any “math facts” or other strategies for doing addition, subtraction or other operations

Direct Modeling: all numbers represented, Direct Modeling: all numbers represented, number order and “verb” are important!number order and “verb” are important!

Child draws or chooses counters to represent the first number in the problem. (e.g. Jen had 3 candies. Then she got 5 more. How many does Jen have now?)

Then child draws or chooses counters to represent the second number.

The child physically moves the two groups together (or circles them, etc.) and counts all, starting with 1.

Word Problems That Involve Word Problems That Involve Action to Direct ModelAction to Direct Model

Join ProblemsJoin Problems (3 types)(3 types)

Result unknown (JRU)Example: Connie had 5 marbles. Juan

gave her 8 more marbles. How many marbles does Connie have now?

Symbolized by 8+5= ?

Join ProblemsJoin Problems

Change unknown (JCU)Example: Connie had 5 marbles. Juan

gave her some more marbles. Now Connie has 13 marbles. How many marbles did Juan give her?

Symbolized by 8+?= 13

Join ProblemsJoin Problems

Start unknown (JSU)Example: Connie had some marbles.

Juan gave her 8 more marbles. Now Connie has 13 marbles. How many marbles did she start with?

Symbolized by ?+8= 13

Separate ProblemsSeparate Problems (3 types)(3 types)

Result unknown (SRU)Example: Connie had 13 marbles. She

gave 5 to Juan. How many marbles does Connie have left?

Symbolized by 13-5= ?

Separate ProblemsSeparate Problems

Change unknown (SCU)Example: Connie had 13 marbles. She

gave some to Juan. Now she has 5 left. How many marbles did she give to Juan?

Symbolized by 13-?= 5

Separate ProblemsSeparate Problems

Start unknown (SSU)Example: Connie had some marbles.

She gave 8 to Juan. Now she has 5 left. How many marbles did she start with?

Symbolized by ? - 8 = 5

Word Problems that Do Not Word Problems that Do Not Involve Action to Direct Model Involve Action to Direct Model (2 kinds)(2 kinds)

Part-Part-Whole Problems (2 Part-Part-Whole Problems (2 types)types)Whole unknown (PPW-WU)Example: Connie has 5 red marbles and

8 blue marbles. How many marbles does she have?

Symbolized by 5+ 8 = ?

Part-Part-Whole Problems (also Part-Part-Whole Problems (also called Equalizing Problems)called Equalizing Problems)Part unknown (PPW-PU)Example: Connie has 13 marbles. 5 are

red, and the rest are blue. How many blue marbles does she have?

Symbolized by 5+ ? = 13

Compare ProblemsCompare Problems (2 types)(2 types)

Difference unknown (CDU)Example: Connie has 13 marbles. Juan

has 5 marbles. How many more marbles does Connie have than Juan?

Compare ProblemsCompare Problems

Compare quantity unknown (C-CQU)Example: Juan has 5 marbles. Connie

has 8 more than Juan. How many marbles does Connie have?

Symbolized (but not precisely) by 5 + 8 = ?

Assignment for next meetingAssignment for next meeting

Briefly describe a children’s story book including author and appropriate age/grade.

Prepare a list of 6 different types of story problems based on that book.

On the back of your paper, identify what kind of problem each one is.

Story Problems from Literature: Story Problems from Literature: An example from a former An example from a former studentstudent

EDUC 406 - EDUC 406 - Math Word ProblemsMath Word Problems

By Tefang Li

ContentsContents

Introduction of the story book

Word Problems

The End

Click the house to read the contents

Old MacDonald Had a Old MacDonald Had a FarmFarm Illustrated by Tracey English Western Publishing Company It’s a counting book. Each time when the song is

repeated with a different animal, one more counting number is added.

At the end, it includes a full page of all the different animals and the counting numbers from 1 to 10.

Click here to go next

Word ProblemWord Problem

Join

Separate

Part-Part-Whole

Compare

Join Type of ProblemsJoin Type of Problems

1. Old MacDonald had 6 hens in the barn and then he bought 5 more hens. How many hens does he have altogether? (Result Unknown, JRU)

2. Old McDonald had some pigs and his friend gave him 2 more pigs. Now he has 15 pigs. How many pigs did he have before he got the 2 new pigs from his friend?

(Start Unknown, JSU)

Separate Type of ProblemsSeparate Type of Problems

1. Old McDonald had 19 sheep. One day, he sold some of his sheep and then he had 11 sheep left. How many sheep did he sell? (Change Unknown, SCU)

2.There were some apples in a basket. The horse ate 3 of them and then there were 9 apples left. How many apples were in the basket in the first place? (Start unknown, SSU)

Part-Part-Whole TypePart-Part-Whole Type

1. Old McDonald owned 21 horses. 4 of them were sleeping and the rest of them were eating. How many horses were eating? (Part unknown, PPW, PU)

2. Old McDonald had some sheep. 7 were black sheep and 8 were white sheep. How many sheep did he have altogether? (Whole unknown, PPW, WU)

Compare TypeCompare Type

1. The horse on his farm ate 14 apples and the cow on his farm ate 6 apples. How many more apples did the horse eat? (Difference Unknown, CDU)

2. The sheep ate 9 apples, and the goat ate 5 more than the sheep. How many apples did the goat eat? (Compare quantity unknown, CCQU)