Evidence-Based Math InstructionDianne 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 InstructionEvidence-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

Explicit Instruction1. Provide Rational & Clear Explanation 2. Model the Learning Process3. Guided Practice4. Application5. Feedback

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How well youHow well you teach = howteach = how

well theywell they learnlearn

NC Adult Education Standards Standards for Mathematical Practice

o Make sense of problems and persevere in solving themo Reason abstractly and quantitativelyo Construct viable arguments and critique the reasoning of otherso Model with mathematicso Use appropriate tools strategicallyo Attend to precisiono Look for and make use of structureo 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

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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?______________________________________________________________________________________________________________________________________________

Left Brain, Right Brain ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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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 Agree1. I cringe when I have to go to math class. 1 2 3 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. 1 2 3 4 5

5. I understand math now, but I worry that it is going to get really difficult soon. 1 2 3 4 5

6. I tend to zone out in math class. 1 2 3 4 5

7. I fear math tests more than any other test. 1 2 3 4 5

8. I do not know how to study for math tests. 1 2 3 4 5

9. It is clear to me in math class, but when I go home it is like I was never there. 1 2 3 4 5

10. I am afraid I will not be able to keep up with the rest of the class. 1 2 3 4 5

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!

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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Math Anxiety Self-Test adapted from Freedman, E. (2003). Mathpower.com. from http://www.mathpower.com/anxtest.htm

Symptoms of Math Anxiety

Psychological: Panic, Paranoia Confusion, Frustration Passive Behavior Lack of Confidence Panic-Stricken Worry Negative Comments Sudden Memory Loss Concepts Not Retained

Physiological: Rapid Heart Beat Sweating Nausea Stomach Disorders Headaches Tired

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? ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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

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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 Explanation Example

IntuitiveAt 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 three-dimensional circles cut into fractional pieces, he/she intuitively begin to arrange them into complete circles, thus seeing the wedges as part of a whole.

Concrete/ Experiential

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.

Pictorial/ Representational

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.

AbstractThe 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.

ApplicationsThe 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.

CommunicationThe 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!

Alternatives to “Drill and Kill”

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Cooperative and Project-based Learning

Change from lecture

Exchange ideas

Connect math to other subjects

Learn different ways to solve problems

Math JournalingUsing 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?

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…

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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 Sometimes Never

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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?”

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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?

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-testNumber 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)

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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.

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Addend Pool 4 7 11 23 31

42 49 62 70

30 70 40 80 70 2080 60 50 70 50 10

050 11

0 10 90 40 50

90 70 130 60 11

0 70

50 20 100 30 12

0 50

70 90 40 100 80 30

Real Life: Dollars, Cents, & Mills1. What is a Mill?

2. Rule for rounding mills: 4 or less, round down; 5 or more, round up.

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

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One Mill = One-tenth of

one cent!

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?_____________________

__________________________________________________________________________________________________________________________________________________

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

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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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.

XXXX

XXXXXXX

XXX

XXXXXX

XXX

Dogs Cats Birds Other 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:

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:

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95 100 103 103 114 114 119

119

122

122

122

122

136 141 144

Mean is118.4

Median is119

Mode is122

Range is95 to 144

Minimum is95

Maximum is 144

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:

87654321

XXXX

XXXXXXX

XXX

XXXXXX

XXX

Dogs

Cats

Birds

Other

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 x3. 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 x4. Create a circle from the strip by connecting/taping the two ends.5. Trace the circle onto your paper.6. Mark off where each category begins and ends7. 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.

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☐Dogs☐Cats☐Birds☐Other☐None

Pets Owned by Members of My Math Class

dogcatbirdsothernone

9. Write a title for your circle graph. 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?

GRAPHIC

ORGANIZER

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  Could Tavares be wrong? Explain

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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

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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. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of Structure.8. 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.

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.

Core Principles for Contextualized Instruction

Relate: Link concepts taught to students’ prior knowledge. Get to know your students.

Experience: Use problem-based learning with hands-on 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.

Teach Using Direct and Explicit Instruction

Rationale: Teachers explain the purpose of instruction and describe key concepts or procedures.

Modeling: Instructors show students demonstrations of procedures or examples of concepts.

Guided Practice: Students practice using the new concepts or procedures, and the instructor provides help as needed.

Independent Practice: Students use the new concepts and procedures on their own.

Monitor: Instructors check students’ understanding and provide appropriate feedback.

Levels of Math Learning

Intuitive: New material is connected to what the student already knows.

Concrete/Experiential: Use manipulatives to introduce, practice, and reinforce concepts.

Pictorial/Representational: Problems are illustrated by pictures or diagrams.

Abstract: A student can now process problems using numbers and symbols.

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.

Sharing

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Online Video Resources

Khan Academy www.kahnacademy.orgKahn 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.htmlThis 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_topicAlthough 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/portalSAS 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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