Evidence-Based Math Instruction
Dianne Barber, barberdb@appstate.edu, Appalachian State University
Welcome, Introductions, Overview
Goals: You will:
 Understand the importance of the Components of Numeracy
 Realize the importance of teaching conceptually first and algorithm last in developing
understanding of math concepts
Objectives: You will:
 Realize that math instruction should address negative feelings toward math before
learning of concepts can take place
 Connect math instruction with content standards
 Learn fun ways to build students’ numeracy skills
 Use real-life activities to make math meaningful
 Have techniques for fostering collaboration and communication in your classroom
 Leave with a variety of strategies to utilize in your classrooms to develop math topics
conceptually for understanding
Activity: My best experience as a student in a math class was __________________
________________________________________________________________
________________________________________________________________________
My worst experience as a student in a math class was _______________________________
________________________________________________________________________
________________________________________________________________________
High Quality Math Instruction
Evidence-based Instructional Strategies
Strategies proven through research to be effective for teaching mathematical skills and
concepts

Explicit instruction

Peer tutoring

Cooperative learning
Standards-based Curriculum

Content and skills believed to be important for students to learn
EBMI, Revised September 4, 2013
Page 1
Explicit Instruction
1. Provide Rational & Clear Explanation
2. Model the Learning Process
3. Guided Practice
4. Application
5. Feedback
NC Adult Education Standards

Standards for Mathematical Practice
o
Make sense of problems and persevere in solving them
o
Reason abstractly and quantitatively
o
Construct viable arguments and critique the reasoning of others
o
Model with mathematics
o
Use appropriate tools strategically
o
Attend to precision
o
Look for and make use of structure
o
Look for and express regularity in repeated reasoning

Number Sense and Operations

Measurement

Geometry

Data Analysis and Probability

Algebra
Best Practices - Increase students’ understanding by

Encouraging student discussion

Presenting and comparing multiple solutions

Using manipulatives

Selecting appropriate instructional tasks

Assessing student understanding
EBMI, Revised September 4, 2013
Page 2
Activity: As a group, work to solve the following problem. Explain your
strategy and the reason you chose that strategy.
One night the King couldn't sleep, so he went down into the Royal kitchen,
where he found a bowl full of mangoes. Being hungry, he took 1/6 of the
mangoes. Later that same night, the Queen was hungry and couldn't sleep.
She, too, found the mangoes and took 1/5 of what the King had left. Still
later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes. Even
later, his brother, the second Prince, ate 1/3 of what was then left. Finally, the third Prince ate
1/2 of what was left, leaving only three mangoes for the servants. How many mangoes were
originally in the bowl?
High Quality Instruction Results In:

Improved student interest and motivation

Greater conceptual understanding

More elaborate and in-depth student discussions about problem-solving processes

Transference of knowledge from one topic to another

Improved student performance on assessments
STUDENTS LEARN MATH BY DOING MATH!
Keys to Success in Math

Positive Attitude

Logical Thinking

Study Skills

Conquer Math Anxiety
Positive Attitude, Self-Belief

Replace Negative Self-talk with Positive Self-talk

“Beliefs, attitudes, and emotions contribute to a person’s ability and willingness to engage
and persevere in mathematics thinking and learning.”
What are some of the beliefs, attitudes, and emotions your students bring to class?
_______________________________________________________________________
_______________________________________________________________________
EBMI, Revised September 4, 2013
Page 3
Left Brain, Right Brain _________________________
___________________________________________
___________________________________________
___________________________________________
___________________________________________
___________________________________________
Math Anxiety
Math Anxiety is ___________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
Do You Have Math Anxiety?
Complete the self-test below to determine your level of math anxiety.
Directions: Rate your answers from 1(disagree) to 5 (agree).
Disagree
1
2
1. I cringe when I have to go to math class.
3
Agree
4
5
2. I am uneasy about going to the board in math class.
1
2
3
4
5
3. I am afraid to ask questions in math class.
1
2
3
4
5
4. I am always worried about being called on in math class.
I understand math now, but I worry that it is going to get really
5.
difficult soon.
6. I tend to zone out in math class.
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
7. I fear math tests more than any other test.
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
8. I do not know how to study for math tests.
It is clear to me in math class, but when I go home it is like I was
9.
never there.
10. I am afraid I will not be able to keep up with the rest of the class.
Add answers to find your total score.
Total Score ________
Check Your Score: 40 – 50 Sure thing, you have math anxiety.
30 – 39 No doubt! You are still fearful about math.
20 – 29 On the fence!
Math Anxiety Self-Test adapted from Freedman, E.
(2003). Mathpower.com. from
http://www.mathpower.com/anxtest.htm
10 – 19 Wow! Very little anxiety here.
Math anxiety is an emotional reaction ... which harms future learning. A good experience …
can overcome these feelings and … future achievement in math can be attained. --Ellen Freedman
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Page 4
Symptoms of Math Anxiety
Psychological:
Physiological:

Panic, Paranoia

Rapid Heart Beat

Confusion, Frustration

Sweating

Passive Behavior

Nausea

Lack of Confidence

Stomach Disorders

Panic-Stricken Worry

Headaches

Negative Comments

Tired

Sudden Memory Loss

Concepts Not Retained
Causes of Math Anxiety

Negative math experience from a person's past

Being punished by a parent or teacher for failing to master a mathematical concept

Being embarrassed in front of a sibling or group of peers

Timed tests and risk of public embarrassment
Math Anxiety is also believed to develop due to the teaching methods used…
Dealing with Math Anxiety

Provide positive reinforcement, build positive attitudes towards math

Re-examine traditional teaching methods


Present lessons in a variety of ways

Make math fun
Teach students to be aware of thoughts, feelings, and actions as they are related to math.

Teach anxiety reduction and management techniques.
What can you do to help alleviate adult students’ math anxiety? ______________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
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Teaching Strategies for Mathematics: Levels of Learning
The term “level” refers to the order that information presented mathematically is processed and learned. Mahesh C.
Sharma, in “Learning Problems in Mathematics: Diagnostic and Remedial Perspectives” states that “almost all mathematics
teaching activities … take place at the abstract level. That is where most textbooks … tests and examinations are.” For
students who have not mastered particular math content, he proposes the following order or “Levels of Math” as effective
for teaching mathematics:
Levels of Learning
Intuitive
Concrete/
Experiential
Pictorial/
Representational
Abstract
Applications
Communication
Explanation
Example
At the intuitive level, new material is connected to
already existing knowledge. (The teacher checks
that the connection is correct.) Introduce each
new fact or concept as an extension of something
the student already knows.
When a student is given threedimensional circles cut into
fractional pieces, he/she
intuitively begin to arrange them
into complete circles, thus seeing
the wedges as part of a whole.
Manipulatives are used to introduce, practice and
re-enforce rules, concepts, and ideas. Present
every new fact or concept through a
concrete model. Encourage students
to continue exploring through asking
other questions.
Using the concrete model (in this case the wedges)
helps the student learn the fractional names. As the
student names the pieces, the instructors asks
questions such as, “How many pieces are needed to
complete the circle? Yes, four, so one out of these
four is one fourth of the circle. As students continue
to explore they may see that two of the quarters
equal half the circle.
A Picture, diagram, or image is used to solve a
problem or prove a theorem. Sketch or illustrate a
model of the new math fact. Pictorial models are
those pictures often provided in textbook
worksheets.
When the student has experienced how some pieces
actually fit into the
whole, present the
relationship in a
pictorial model, such
as a worksheet.
The student is able to process symbols and
formulae. Show students the new fact in symbolic
(numerical) form.
After the student has the concrete and pictorial
models to relate to, he can understand that 1/4 + 1/4
is not 2/8. Until this concept has been developed, the
written fraction is meaningless to the student.
The student is able to apply a previously learned
concept to another topic. Ask student to apply the
concept to a real-life situation. The student can
now approach fractions with an understanding
that each fraction is a particular part of a whole.
The instructor can now introduce word problems
without illustrations because students have images
in their heads.
A student who is asked to give a real-life example or
situation might respond with 1/4 cup of flour + 1/4
cup of flour equals 1/2 cup of flour.
The student is able to convey knowledge to
another student reflecting an embedded
understanding and the highest level of learning.
The student’s success in this task reflects an
embedded understanding and the highest level of
learning.
Ask students to convey their knowledge to other
students, i.e., students must translate their
understanding into their own words to express what
they know.
The mastery of a given mathematical concept passes from the intuitive level of understanding to the level where
the student can explain how he has arrived at a particular result and can explain the intricacies and the concept.
Beginning at the abstract level may create math anxiety.
Connect to background knowledge, dendrites grow from existing dendrites!
EBMI, Revised September 4, 2013
Page 6
Alternatives to “Drill and Kill”
Cooperative and Project-based Learning

Change from lecture

Exchange ideas

Connect math to other subjects

Learn different ways to solve problems
Math Journaling
Using Affective/Attitudinal Prompts in Math Journals: Many adult learners are fearful of trying and failing to solve
problems. Their own feelings of inability to learn mathematics get in their way and, in essence, become a self-fulfilling
prophecy. The more anxious the learner becomes, the less he/she is able to focus on the math content.
Affective/attitudinal math journal prompts enable students to express their feelings, concerns, and fears about
mathematics. The following are examples of affective/attitudinal prompts:




Explain how you feel when you begin a math session.
One secret I have about math is…
If I become better at math, I can…
My best experience with math was when…



My worst experience with math was when…
Describe how it feels if you have to show your work on
the board…
One math activity that I really enjoyed was…
Using Content Prompts in Math Journals: When working with math content, most adult learners expect merely to perform
a series of computations and provide a specific answer. Rarely have they been asked to explain what they did to find an
answer. Mathematical content prompts provide learners with an opportunity to explain how they arrived at a specific
answer, thus enabling them to begin making connections between what they have done and the math content itself. These
types of prompts also enable students to support their point of view or to explain errors they made in their calculations.
The following are examples of content prompts:




The difference between … and … is…
How do you…?
What patterns did you find in…?
How do you use … in everyday life?



Explain in your own words what … means.
One thing I have to remember with this kind of
problem is…
Why do you have to…?
Using Process Prompts in Math Journals: Process prompts allow learners to explore how they go about solving a problem.
It moves them from mere computations to looking at math problem solving as a process that, just as in solving real-life
problems, requires a series of steps and questions that must be analyzed and answered. Process prompts require learners
to look more closely at how they think. The following are examples of process prompts:





How did you reach the answer for the problem
about…?
What part in solving the problem was the easiest?
What was the most difficult? Why?
The most important part of solving this problem was…
Provide instructions for a fellow student to use to
solve a similar problem.
What would happen if you missed a step in the
problem? Why?
EBMI, Revised September 4, 2013






When I see a word problem, the first thing I do is…
Review what you did today and explain how it is
similar to something you already knew.
Is there a shortcut for finding…? What is it?
Could you find another way to solve this problem?
I draw pictures or tables to solve problems because…
The first answer I found for this problem was not
reasonable, so I had to…
Page 7
Contextualized Instruction

Real Life

Careers

Higher Learning
Self-Test: Are You Teaching Contextually?
Take this self-test and see. These standards appear to some degree in almost all teaching, but contextualized
instruction is always rich in all ten standards.
Always
1.
Are new concepts presented in real-life (outside the classroom)
situations and experiences that are familiar to the student?
2.
Are concepts in examples and student exercises presented in the
context of their use?
3.
Are new concepts presented in the context of what the student already
knows?
4.
Do examples and student exercises include many real, believable
problem-solving situations that students can recognize as being
important to their current or possible future lives?
5.
Do examples and student exercises cultivate an attitude that says, "I
need to learn this?”
6.
Do students gather and analyze their own data as they are guided in
discovery of the important concepts?
7.
Are opportunities presented for students to gather and analyze their
own data for enrichment and extension?
8.
Do lessons and activities encourage the student to apply concepts and
information in useful contexts, projecting the student into imagined
futures (e.g., possible careers) and unfamiliar locations (e.g.,
workplaces)?
9.
Are students expected to participate regularly in interactive groups
where sharing, communicating, and responding to the important
concepts and decision-making occur?
Sometimes
Never
10. Do lessons, exercises, and labs improve students’ reading and other
communication skills in addition to mathematical reasoning and
achievement?
Adapted from: www.cord.org/contextual-teaching-self-test
EBMI, Revised September 4, 2013
Page 8
Number Sense and Operations

Clothesline Math: Whole Numbers, Fractions, Decimals

Mental Math with Dice

Fraction Strips

Basic Calculator Operations Cross Number Puzzle (ABSPD Calculator Manual)

Card Games (ABSPD Numeracy Manual)

Rounding in a Row and other Games (ABSPD Numeracy Manual)

Contextualized: Dollars, Cents, & Mills (ABSPD Teaching Math Contextually Manual)
Note: All manuals can be downloaded from the ABSPD website: www.abspd.appstate.edu
Rounding in a Row – Addition
Directions: Choose two numbers from the “Addend Pool,” add the numbers, round to the nearest 10, and cover/mark your
answer if it is not already covered. The first player to have four in a row, horizontally, vertically, or diagonally, wins. See
next page for game.
EBMI, Revised September 4, 2013
Page 9
Addend Pool
4
7
42
11
49
23
62
31
70
30 70 40 80 70 20
80 60 50 70 50 100
50 110 10 90 40 50
90 70 130 60 110 70
50 20 100 30 120 50
70 90 40 100 80 30
Real Life: Dollars, Cents, & Mills
1. What is a Mill?
2. Rule for rounding mills: 4 or less, round down; 5 or more, round up.
One Mill =
One-tenth of
one cent!
3. How many mills are in 1 cent?
4. How many mills are in 10 cents?
5. How many mills are in $1.00?
6. Round to the nearest cent:
a. $0.012
b. $0.537
c. $4.485
7. What are some real-life context where the mill is used? Could a person or company make
additional profit based on how they rounded to the nearest cent?_____________________
_________________________________________________________________________
_________________________________________________________________________
EBMI, Revised September 4, 2013
Page 10
Measurement and Geometry

Working with Angles & Triangles



Acute, Obtuse, Equilateral, Right, Degrees
Measurement

Linear, Area, Volume, Surface Area

Circumference, Diameter, Calculate Pi
Contextualize by having students do real-life measurments
Data Analysis

Frequency Graphs

Bar Graphs

Circle Graphs

Contextualize by using real-life data
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
EBMI, Revised September 4, 2013
Page 11
Creating a Frequency Graph or Table
When working with nominal data, create an easy-to-use frequency graph by making a line. Use equal-size x’s
and equal spacing for each category. Line up your x’s or use graph paper so it is easy to note which category
contains the most data items. Some people can look at a frequency graph and make true statements by
“eyeballing,” or visually estimating, the size of each category. With the data below the only measure of central
tendency that can be determined is mode.
X
X
X
X
X
X
X
Cats
X
X
X
X
Dogs
X
X
X
X
X
X
Other
X
X
X
Birds
X
X
X
None
When working with interval (number) data you can find measures of central tendency (mean, median, mode)
and range. It is important to put the data in order from smallest to largest. The data can arranged in one row or
one column. For example: If you had the following IQ scores: 122, 103, 119, 114, 122, 122, 141, 119, 100, 114,
144, 122, 95, 136, 103 the data could be arranged in one row as follows:
If you are working with a larger amount of data you may want to arrange the data in a frequency table and use
tally marks. For example, using the following data for 20 students:
95
100
Mean is
118.4
103
103
114
Median is
119
114
119
Mode is
122
119
122
122
Range is
95 to 144
122
122
Minimum is
95
136
141
144
Maximum is
144
The marks awarded for an assignment set for a Year 8 class of 20 students
were as follows:
6 7 5 7 7 8 7 6 9 7
4 10 6 8 8 9 5 6 4 8
To construct a frequency table, proceed as follows:
Step 1: Construct a table with three columns. The first column shows what is
being arranged in ascending order (the marks). The lowest mark is 4. So, start
from 4 in the first column as shown.
Step 2: Go through the list of marks. The first mark in the list is 6, so put a
tally mark against 6 in the second column. The second mark in the list is 7, so
put a tally mark against 7 in the second column. The third mark in the list is 5,
so put a tally mark against 5 in the third column as shown. Continue this
process until all marks in the list are tallied.
Step 3: Count the number of tally marks for each mark and write it in third
column. The finished frequency table is as follows:
EBMI, Revised September 4, 2013
Page 12
Constructing a Bar Graph
1. Determine the following elements of the bar graph from the frequency table
o Title of the graph.
o Label for each axis--Here we must determine which is to be the frequency axis and which is to be
the grouped data axis.
o Scale for each axis--Determine the numerical scale for the frequency axis, then the group names for
grouped data axis.
2. Draw a set of axes that you will use to construct your graph
o Determine which axis will be the frequency axis--Determine whether bars will go horizontally or
vertically.
o Write in axes labels.
o For the frequency axis, determine the scale interval.
3. Use the data from the table to draw in the bars on the graph.
Examples:
☐Dogs
8
7
X
☐Cats
6
X
X
☐Birds
5
X
X
☐Other
4
X
X
X
☐None
3
X
X
X
X
X
2
1
X
X
Dogs
X
X
Cats
X
X
Birds
X
X
Other
X
X
None
Pets Owned by Members of My Math Class
Constructing a Circle Graph/Pie Chart from a Bar Graph
1. Make a copy of the bar graph you created. If each bar is not already a different color, then color each bar a
different color.
2. Cut out the bars.
x x x x
x x x
x x x x x x x
x x x
x x x x x x
3. Tape the bars together, creating one long strip.
x x x x x x x x x x x x x x x x x x x x x x x
4.
5.
6.
7.
Create a circle from the strip by connecting/taping the two ends.
Trace the circle onto your paper.
Mark off where each category begins and ends
Draw a line from the center of the circle to the edge of the circle, creating
pie slices for each different section.
8. To keep track of the data, establish a legend or key, using one color for
each bar (pie section). Record the legend next to the circle.
9. Write a title for your circle graph.
EBMI, Revised September 4, 2013
Pets Owned by Members of
My Math Class
dog
cat
birds
other
none
Page 13
Algebra

Clothesline Math: Negative Numbers, Exponents & Roots

Exponents & Roots

Word Problem: Extraneous Information, Multi-Step, Problem Solving Graphic Organizer
1. One package of cards costs $17.00. There are 72 cards in each package. How many cards are in 8 packages?
2. The school is planning a field trip. The school has 8 classrooms. There are 305 students in the school and 61
seats on each school bus. How many buses are needed to take the trip?
3. Calvin paints pictures and sells them at shows. He charges $56.25 for a large painting, $37.50 for a medium
painting and $25.80 for a small painting. Last month he sold six large paintings and three small painting.
How much did he make in all?
4. On Thursday the Meat King Market sold 210 pounds of ground beef. On Friday they sold twice that amount.
On Saturday they sold 130 pounds. On Sunday they sold 63 pounds. How much more meat did they sell on
Friday than Saturday?
5. Jan bought 4 pair of shoes that were 25% off. How much did Jan pay for the pair of shoes that was originally
priced at $75?
G
R
A
P
H
I
C
O
R
G
A
N
I
Z
E
R
Question
Draw a Picture/Graph/Table
Important Facts
Extra Information
Equation (number sentence)
Estimation (without computing)
Computation
Answer Sentence
Use Real Life Math: Trevor bought 2 items on sale. One item was 10% off and the other item
was 20% off. He says he saved 15% altogether.
Could Tavares be right? Explain
EBMI, Revised September 4, 2013
Page 14
Could Tavares be wrong? Explain
EBMI, Revised September 4, 2013
Page 15
Components of Numeracy
CONTEXT – the use and purpose for which an adult takes on a task with mathematical demands
Family or Personal—as a parent, household manager, consumer, financial and health-care decision
maker, and hobbyist
Workplace—as a worker able to perform tasks on the job and to be prepared to adapt to new
employment demands
Further Learning—as one interested in the more formal aspects of mathematics necessary for further
education or training
Community—as a citizen making interpretations of social situations with mathematical aspects
such as the environment, crime, and politics
CONTENT – the mathematical knowledge that is necessary for the tasks confronted
Number and Operation Sense—a sense of how numbers and operations work and how they relate
to the world situations that they represent
Patterns, Functions and Algebra—an ability to analyze relationships and change among quantities,
generalize and represent them in different ways, and develop solution methods based on the
properties of numbers, operations, and equations
Measurement and Shape—knowledge of the attributes of shapes, how to estimate and/or determine
the measure of these attributes directly or indirectly, and how to reason spatially
Data, Statistics and Probability—the ability to describe populations, deal with uncertainty, assess
claims, and make decisions thoughtfully
COGNITIVE AND AFFECTIVE—the processes that enable an individual to solve problems and, thereby,
link the content and the context
Conceptual Understanding—an integrated and functional grasp of mathematical ideas
Adaptive Reasoning—the capacity to think logically about the relationships among concepts and
situations
Strategic Competence—the ability to formulate mathematical problems, represent them, and solve
them
Procedural Fluency—the ability to perform calculations efficiently and accurately by using paper and
pencil procedures, mental mathematics, estimation techniques, and technological aids
Productive Disposition—the beliefs, attitudes, and emotions that contribute to a person’s ability and
willingness to engage, use, and persevere in mathematical thinking and learning or in activities with
numeracy aspects
From Ginsburg, L., Manly, M., and Schmitt, M. J. (2006). The components of numeracy [NCSALL Occasional Paper]. Cambridge, MA:
National Center for Study of Adult Literacy and Learning. Available:
http://www.ncsall.net/fileadmin/resources/research/op_numeracy.pdf
EBMI, Revised September 4, 2013
Page 16
NC Adult Education Standards and Standards for Mathematical Practice
The eight Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels
should seek to develop in their students:
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of Structure.
Look for and express regularity in repeated reasoning.
Webb’s Depth of Knowledge Levels
Level 1-Recall
Conduct basic mathematical calculations, measure,
perform routine procedures or a clearly defined series of
steps.
Level 2-Skills/Concept
Solve routine multi-step problems, organize and display
data in tables, graphs and charts, estimate, identify
patterns.
Level 3-Strategic Thinking
Reason, plan, explain and justify, make conjectures,
develop a logical argument, supporting ideas with details
and examples, apply a concept in other contexts.
Core Principles for Contextualized Instruction
Relate: Link concepts taught to students’ prior
knowledge. Get to know your students.
Experience: Use problem-based learning with handson activities using workplace situations, problems, and
materials to make learning real.
Apply: Use real-life situations and meaningful
authentic materials to create lessons around skills
students need to acquire to accomplish their goals.
Cooperate: Use thematic, project-based, collaborative
and multi-level learning to have students work as a
team to achieve a goal.
Transfer: Use what is learned in one area and
practice/apply it in other areas.
Level 4-Extended Thinking
Use complex reasoning, relate ideas within a content area
or across content areas, design a mathematical model to
solve a practical or abstract situation.
Teach Using Direct and Explicit Instruction
Levels of Math Learning
Rationale: Teachers explain the purpose of instruction and
describe key concepts or procedures.
Intuitive: New material is connected to what the
student already knows.
Modeling: Instructors show students demonstrations of
procedures or examples of concepts.
Concrete/Experiential: Use manipulatives to
introduce, practice, and reinforce concepts.
Guided Practice: Students practice using the new concepts
or procedures, and the instructor provides help as needed.
Pictorial/Representational: Problems are illustrated
by pictures or diagrams.
Independent Practice: Students use the new concepts and
procedures on their own.
Abstract: A student can now process problems using
numbers and symbols.
Monitor: Instructors check students’ understanding and
provide appropriate feedback.
Application: A student uses a math concept in a real
life situation.
Communication: A student truly understands a
problem when he/she can explain the solution to
someone else.
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Sharing
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Online Video Resources
Khan Academy
www.kahnacademy.org
Kahn Academy includes hundreds of free, screen –captured instructional videos from arithmetic to Algebra II. Kahn
Academy has a sophisticated management information system that can be used by learners, teachers, or tutors. A teacher
can assign a video and quiz for homework before a class, reversing the typical class activities and homework order. Then,
when students arrive for class, the teacher knows who is comfortable with the subject matter and is ready to move on, who
needs a little more help, and who requires a thorough review. With this information, the teacher is able to provide
customized help to the students who need it. This can enable mastery learning where students learn at a personalized pace.
National Library of Virtual Manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
This site has extensive online algebra manipulatives across many grade levels to help students learn concepts like equations,
graphing, patterns, and functions.
Math TV
www.mathtv.com/videos_by_topic
Although Math TV is a (low-cost) commercial website, the instructional videos are free. They include instruction on subjects
from whole numbers to fractions, decimals, and percentages to algebra, geometry, trigonometry, and calculus. Each
problem features at least two different explanations (usually four) by different people. There are also explanations in
Spanish for most of the videos.
SAS Curriculum Pathways
http://www.sascurriculumpathways.com/portal
SAS Curriculum Pathways provides a free math and Algebra 1 curriculum aligned to the common core. This site contains
“more than 200 Interactive Tools, 200 Inquiries, 600 Web Lessons, and 70 Audio Tutorials that provide technology-rich
instruction and develop higher-order thinking skills. These resources target grades 6-12.” (SAS Website). The Algebra 1
“course engages students through real-world examples, images, animations, videos and targeted feedback. Teachers can
integrate individual components or use the entire course as the foundation for their Algebra 1 curriculum.” (SAS Press
Release 8/8/12)
Adapted from Rosen, David (2012). Learn mathematics by watching videos. Journal of Research and Practice for Adult Literacy, Secondary,
and Basic Education, 1(2).
Thanks for Making a Difference!
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