Overarching Goal for Reading/Learning Math in RDG 185 The learner will employ thinking reading strategies for developing competence in math.

Research: By learning in ways that develop competence in math, students can more readily apply math knowledge acquired in one context to another context; math becomes useful beyond the math course. If math is not learned using cognitive strategies that develop competence, math procedures are quickly forgotten.

The following slides introduce learning strategies for developing competence in math as one is learning.

How to Read to Learn Math

Overarching Goal for Reading/Learning Math in RDG 185 The learner will employ thinking reading strategies for developing competence in math.

In order to develop competence in math the learner needs to: (1) develop a deep foundation of factual knowledge, (2) understand facts and ideas in the context of a conceptual framework, and (3) organize knowledge in ways that facilitate retrieval and application.

When reading math textbooks, the reader should be looking for

• new terminology, and

• examples of that terminology from real life,

• steps in procedures and

• the math terminology used to explain the procedures

• along with examples of each step of the procedure from real life.

In order to develop competence in math the learner needs to: (1) develop a deep foundation of factual knowledge, (2) understand facts and ideas in the context of a conceptual framework, and (3) organize knowledge in ways that facilitate retrieval and application.

(1) develop a deep foundation of factual knowledge

Math has a lot of factual knowledge to know. If we look over Chapter 14, p. 349- on Fractions and Mixed Numbers, we will quickly see that there is a lot of math vocabulary that must be understood to read the chapter. For example:

Math Terminology in the Fractions and Mixed Numbers chapter: EXAMPLE: fraction, whole unit,, numerator, denominator, whole number, denominator,, fraction bar, solution, properties of fractions, fractional part of a whole

(1) Strategy for developing a deep foundation of factual knowledge.

Create a mind map that organize math concepts (math vocabulary) with illustrations of each concept as they are encountered while reading math textbook.

Strategy for developing a deep foundation of factual knowledge.

Create a mind map that organizes the math concepts (math vocabulary) with illustrations of each concept.

Example: Under “Definition of Fractions” on page 350, we encounter the following math vocabulary: whole number, fraction, numerator, denominator, fraction bar,

Definition of a

Fraction

Whole numberNumber with no parts

Ex. 1 whole apple

fractionwhole divided in to equal parts

Ex. circle divided into 4 parts

numerator

denominator

fraction bar

In order to develop competence in math the learner needs to: (1) develop a deep foundation of factual knowledge, (2) understand facts and ideas in the context of a conceptual framework, and (3) organize knowledge in ways that facilitate retrieval and application.

(2) understand facts and ideas in the context of a conceptual framework

When we systematically organize the concepts in the chapter, we develop a conceptual framework. Fortunately, the textbook’s author has done that for us under the title, Fractions and Mixed Numbers, the headings and subheadings. The conceptual framework for chapter 14 is Fractions and Mixed Numbers and the concepts related to Fractions and Mixed Numbers are all the math vocabulary, and steps required to solve problems.

In order to develop competence in math the learner needs to: (1) develop a deep foundation of factual knowledge, (2) understand facts and ideas in the context of a conceptual framework, and (3) organize knowledge in ways that facilitate retrieval and application.

(2) understand facts and ideas in the context of a conceptual framework

When we systematically organize the concepts in the chapter, we develop a conceptual framework. Fortunately, the textbook’s author has done that for us under the title, Fractions and Mixed Numbers, the headings and subheadings. The conceptual framework for chapter 14 is Fractions and Mixed Numbers and the concepts related to Fractions and Mixed Numbers are all the math vocabulary, and steps required to solve problems.

Strategy for understanding facts and ideas in the context of a conceptual framework.

Create a mind map that organizes the math concepts (math vocabulary) with illustrations of each concept.

Example: Under “Changing Mixed Number to an Improper Fraction” on page 353, we encounter the following math vocabulary (concepts), and operations (multiplication and addition) for the steps in procedure of making the change for 3 1/2:

Strategy for understanding facts and ideas in the context of a conceptual framework and organizing knowledge in ways that facilitate retrieval and application.

Create a mind map that organizes the math concepts (math vocabulary) with illustrations of each concept.

Changing Mixed Number

to Improper Fraction

1. Multiply whole number by denominator

3 x 2 = 6 (6 is the product)

2. Add the result (product) to

the numerator

6 + 1 = 7 (7 is the sum)3. Place the result (sum)

of step 2 over the

denominator

7/2

Mind Mapping Math Knowledge, Procedures and Concepts Mind Mapping for a Procedure The name of the math procedure should be the center of the map (ex. Writing Mixed Numbers (2 ½) as an Improper Fraction).Each main branch off the center of the map should have printed on it a step in the procedure being learned using math language. (Ex. Multiply the denominator of the fraction by the whole number. Hint: use abbreviations)Off each main branch should be examples of the numbers and symbols representing the step being learned. (ex. 2 ½, write 2 X 2 = 4)Also, off the main branch should be a drawing of a concrete example representing the concept being learned. (ex. Draw 3 cookies being cut in half) Mind Mapping for a Concept The name of the main concepts in the reading selection should be in the center of the map (ex. Proper Fractions, Improper Fractions and Mixed Numbers)Each main branch off the center of the map should have printed on it new terminology (ex. Proper fraction)Off of each main branch should be examples of number representing new words. (ex. Proper fraction 2/3; Improper fraction 7/5; Mixed number 2 ¼Also off each branch should be a drawing of a concrete example representing the new terminology. (ex. For Mixed number, draw three pizzas and one ¼th slices of pizza for 3 ¼.

Using Rules of Consolidation When New Math Information is Found 1. Deliberately re-expose yourself to the information if you want to retrieve it later. 2. Deliberately re-expose yourself to the information more elaborately if you want the retrieval to be of higher quality. “More elaborately” means thinking, talking or writing about what was just read. Any mental activity in which the reader slows down and mentally tries to connect what they are reading to what they already know is elaboration. (It is very important to try and find real life examples in the text at this time.) 3. Deliberately re-expose yourself to the information more elaborately, and in fixed intervals, if you want the retrieval to be the most vivid it can be. (Medina) Fixed Time Intervals for Re-exposing and Elaborating • As the reader identifies what is important while reading, stop re-expose yourself to the information

and elaborate on the it (have an internal dialogue, what do you already know about what you are reading, write about it (take notes in your own words), explain it to yourself out loud.

• When you come to a new topic or paragraph, explain to yourself what you have just read; this is re-exposure to the information.

• When you finish studying, take a few minutes to re-expose yourself to the information and elaborate.

• Within 90 minutes to 2 hours, re-expose yourself to the information and elaborate.• Review again the next day as soon as you can

Internal Dialogue with Math Concepts and Procedures It is important that math students learn to have an ongoing internal dialogue (mental conversation with themselves) as they are learning mew math concepts and procedures. It is common for math students to passively watch instructors work problems on the board and mimic what they saw while doing their homework. There is almost no way for these students to actually learn math in any way that ensures application in the future.