MAXIMIZE ALL STUDENTS MATHEMATICAL LEARNING IN …...maximize all students’ mathematical learning...

MAXIMIZE ALL STUDENTS’ MATHEMATICAL LEARNINGIN INCLUSIVE SECONDARYCLASSROOMS THROUGHTHE USE OF POWERFUL

INSTRUCTIONALSTRATEGIES & TECHNIQUESMARCH 30, 2016

PART 1 OF 2

Paul J. Riccomini, Ph.D.

[email protected]

@pjr146

Maximize Students’ Mathematical LearningMS/HS

March 30, 2016Part 1 of 2

© Paul J. Riccomini [email protected] 1

Topics• Designing instruction to help students of all skill levels achieve success in mathematics.

• NMAP, 2008 Final Report‐OVERVIEW

–Working memory and impact on learning

• Instructional Techniques & Strategies

1. Fractions

2. Interleave Worked Solution Strategy (IWSS)

3. Spaced Learning Over Time (SLOT)

• Conclusion & Wrap Up© Paul J. Riccomini 2016

[email protected]

Components of Effective Mathematics Programs

Mathematics Curriculum & Interventions

Assessment & Data-Based Decisions

Teacher Content &

Instructional Knowledge

100% Math Proficiency

© Paul J. Riccomini [email protected]

Mathematics Performance

Translated to Real World Performance

• 78% of adults cannot explain how to compute interest paid on a loan

• 71% cannot calculate miles per gallon

• 58% cannot calculate a 10% tip

Mathematics Advisory Panel Final Report, 2008






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Math Proficiency of U.S. Students

• International comparisons

• Low fractions of proficiency on NAEP

• Falling proficiency at higher grades

• Heavy remedial demand upon entry into college

• Achievement gap

Algebra as a gateway


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Math Proficiency of U.S. StudentsLow fractions of proficiency on NAEP

– Discuss the challenges/difficulties that your students experience with fractions both conceptual and mechanical (procedural manipulation?

1.

2.

3.

4.

– Why?????????


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Math Proficiency of U.S. Students• Low fractions of proficiency on NAEP

• Teachers anchor the development of whole numbers with the visual representation of a Number Line.– Very important because the number line clearly demonstrated

quantity

– Visually shows that numbers have specific locations on a number line

http://www.mathsisfun.com/number‐line.html





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• As teachers begin to introduce fractions...the number line vanishes and the concepts of fractions are anchored by a circle– Circle does not demonstrate that a fraction is a number and that it

has a location on a number line

– Circles do not clearly demonstrate the quantity of fractions compared to other fractions

• A number line displaying fractions is very important to the conceptual understanding


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–Use number line representations to help students recognize fractions are numbers and that they expand the number system


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–Use number line representations to help students recognize fractions are numbers and that they expand the number system





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Breakout Activity‐(HO #1c)Fractions and the Number line

• Discuss your current curricular materials in relationship to the use of the number line to represent fractions, decimals, and percents.– Is the # line a common representation?

– Are fractions and decimals ever displayed together on a # line?

– How often are students exposed to the number line with fractions?• During computation instruction???

– What types of activities involve the # line?

• Where can the # line be used more frequently in your math lessons in conjunction with fractions?

– Whole group, small group centers or stations, etc?

Foundations for SuccessNational Mathematics Advisory Panel

Final Report, March 2008

Select Slides taken from the NMAP-Final Report Presentation available at: http://www.ed.gov/MathPanel

Learning Processes‐NMAP‐2008

• To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, factual knowledge and problem solving skills.

• Limitations in the ability to keep many things in mind (working‐memory) can hinder mathematics performance.

‐ Practice can offset this through automatic recall, which results in less information to keep in mind and frees attention for new aspects of material at hand.

‐ Learning is most effective when practice is combined with instruction on related concepts.

‐ Conceptual understanding promotes transfer of learning to new problems and better long‐term retention.

NMAP, 2008





Instructional Practices‐NMAP‐2008

Research on students who are low achievers, have difficulties in mathematics, or have learning disabilitiesrelated to mathematics tells us that the effective practice includes:

Explicit methods of instruction available on a regular basis

Clear problem solving models

Carefully orchestrated examples/ sequences of examples.

Concrete objects to understand abstract representations and notation.

Participatory thinking aloud by students and teachers.



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For More Information

Please visit us online at:http://www.ed.gov/MathPanel

• Read it! Fact Sheet SH#1d

• The report and Factsheet should be on the desk of every teacher responsible for teaching and planning math.


Learner Characteristics• Strategic Learners

– Able to analyze a problem and develop a plan – Able to organize multiple goals and switch flexibly from simple to more complicated goals

– Access their background knowledge and apply it to novel tasks

– Develop new organizational or procedural strategies as the task becomes more complex

– Use effective self‐regulated strategies while completing a task

– Attribute high grades to their hard work and good study habits

– Review the task‐oriented‐goals and determine whether they have been met

http://iris.peabody.vanderbilt.edu/srs/chalcycle.htm





Learner Characteristics• Non‐Strategic Learners

– Unorganized, impulsive, unaware of where to begin an assignment

– Unaware of possible steps to break the problem into a manageable task, possibly due to the magnitude of the task

– Exhibit problems with memory

– Unable to focus on a task

– Lack persistence

– Experience feelings of frustration, failure, or anxiety

– Attribute failure to uncontrollable factors (e.g., luck, teacher's instructional style)


Essential Question for Teachers

• Essential Question

–What did I do “instructionally different” to support learning for the struggling students?

• Asked during instructional planning and after instructional delivery!!!


• Interleaved Worked Solution Strategy• Interleaved Worked Solution Strategy1

• Spaced Learning Over Time (SLOT)• Spaced Learning Over Time (SLOT)2

Strategies & Techniques





CCSS for Mathematical Practices1. Make sense of complex 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.

(CCSS, 2010)


Learning Outcomes of CCSS‐MP

(McCallum, 2011)


Breakout Activity

• Discuss the following questions:

1. What do you do to help students complete:

• Homework

• Independent practice opportunities

• Study for tests & Quizzes (e.g., study guides)

• Review important skills

2. What do you do to help students remember important information from previous lessons throughout the course of the academic year?





Excellent Resource: IES

• Institute of Education Science

– Review research to determine instructional strategies and techniques that are supported by high quality evidence

http://ies.ed.gov/



Learner Characteristics• Non‐Strategic Learners

– Unorganized, impulsive, unaware of where to begin an assignment

– Unaware of possible steps to break the problem into a manageable task, possibly due to the magnitude of the task

– Exhibit problems with memory

– Unable to focus on a task

– Lack persistence

– Experience feelings of frustration, failure, or anxiety

– Attribute failure to uncontrollable factors (e.g., luck, teacher's instructional style)


Instructional Practices‐NMAP‐2008Research on students who are low achievers, have difficulties in mathematics, or have learning disabilitiesrelated to mathematics tells us that the effective practice includes:

Explicit methods of instruction available on a regular basis

Clear problem solving models

Carefully orchestrated examples/ sequences of examples.

Concrete objects to understand abstract representations and notation.

Participatory thinking aloud by students and teachers.


NMAP, 2008





Interleave Worked Solution Strategy

• Interleave worked example solutions and problem‐solving exercise

• Literally, alternate between worked examples demonstrating one possible solution path and problems that the student is asked to solve independently

• This can markedly enhances student learning

IES Practice Guide, (2007, September)


• Typical Math Homework assignment

– Pg. 155 #1‐21 odd

• Students are required to solve all problems.




• Interleaved Homework assignment

– Pg 155 1‐10 (all)

– Odd problems





Typical Practice with Fractions



• Other considerations:1. The amount of guidance an annotation

accompanying the worked out examples varies depending on the situation

2. Gradually fade examples into problems by giving early steps in a problem and requiring students to solve more of the later steps

3. Use examples and problems that involve greater variability from one example or problem to the next• Changing both values included in the problem and the

problem formats.


• IWSS Practice 4b




• IWSS Practice Exercise

– Worked Solutions continue to alternate throughout the practice exercise

– Unsolved problems for students to practice continues to alternate

– Practice Exercise ends with a solution that the students has to explain.

IWSS #4c

• Example of implementing the IWSS strategy into Algebra Homework.

• Students must be prompted to study the solution

• One Complete Solution #1

• Solution begins to fade in #3 and #5

• Only one Step is provided in #7

• No solutions are provided





• During Whole Class instruction1. Start off discussion around an already solved problem

• Pointing out critical features of the problem solution

2. After discussion have students pair off in small groups or work individually to solve a problem (JUST ONE!) on their own

3. Then back to studying an example, maybe one students present their solutions and have others attempt to explain

4. Then after studying the solved example, students are given another problem to try on their own.



Using Worked out Examples in Class

• Solved problems show both the problem and solution steps• Can be created by teacher, or taken from a textbook or other curricular

materials• Can include annotations describing the steps

• Provide annotations to the above solved problem.


Using Worked out Examples in Class (HO#4d)

• Solved problems show both the problem and solution steps• Can be created by teacher, or taken from a textbook or other curricular

materials• Can include annotations describing the steps

• Provide annotations to the above solved problem.


1. 2.3.4.5.




Instructional Planning Breakout (SH #4e)

• Modify the Algebraic Equations Worksheet to include worked out examples following the IWSS guidelines.

• Remember there is no “EXACT” structure for IWSS. Base it on your experience, the students’ instructional needs, and the target content.

• Each group will exchange their IWSS sheets for review by another group.

Implementation Ideas‐IWSS

• Have students alternate between reading already worked solutions and trying to solve problems on their own

• As students develop greater expertise, reduce the number of worked examples provided and increase the number of problems that students solve independently



Classroom Application Activity‐IWSSHO #4f

• Teach learners how to use the solutions included with the IWSS.– How will you teach the learners to use the solutions?

– How will you model the process of studying a solution?

– How will you provide feedback during the initial stages of learning the IWSS strategy?

– How will you provide opportunities to practice studying the solution?

• What are the essential steps when reviewing a solution?

• What are key questions that you want the learners to ask and answer when reviewing the solution?





Classroom Application Activity‐IWSS

• Identifying materials that you will use in an upcoming chapter/unit that best fits IWSS.

• Modify or adapt those materials to incorporate the IWSS technique.

• If you have already developed materials using the IWSS technique, review those materials and check for fidelity of the materials.

• Each group will be asked to provide an example of materials with the IWSS technique.


IWSS Homework for May 10th

• Identify a problem type that is appropriate for the IWS Strategy (multi‐step task).

• Develop a Classroom Activity where students are using the solution to first rehearse (practice) the process and then solve a similar problem without a solution.

• Bring the developed activity back on May 10.


• Interleaved Worked Solution Strategy• Interleaved Worked Solution Strategy1

•Spaced Learning Over Time (SLOT)•Spaced Learning Over Time (SLOT)

2

Strategies & Techniques






Space Learning Over Time

• Arrange for students to have spaced instructional review of key course concepts through the SLOT Strategy– At least 2 times/year

– Separated by several weeks to several months

• Why:– Helps student remember key facts, concepts, and knowledge



Spaced Learning Over Time

• Make sure important and essential curriculum content is reviewed at least 3‐4 weeks after it was initially taught.

• Benefits of a delayed review is much greater than the same amount of time spent reviewing shortly after initial instruction (Rohrer & Taylor, 2006).



Space Learning Over Time (HO#5)





Fast forward 4‐6 weeks from when identified skills were taught & list date here to revisit

Space Learning Over Time (HO#5)

Important Consideration:• Concepts and/or skills identified

in the first two cells should be revised at least TWO times before the end of the year.

• For example, if you revisit a concept/skill beginning of October, it needs to be revisited at least one more time in January/February

Implementation Ideas‐SLOT

• Identify key concepts, terms, and skills taught and learned during each 6 week unit

• Arrange for students to be re‐exposed to each Big Idea on at least two occasions, separated by a period of at least 4‐6 weeks.

• Arrange homework, quizzes, and exams in away that promotes delayed reviewing of important course content



Classroom Application Activity‐SLOT

• Using the spaced instructional review sheet, divide the school year into 6 week units starting at the beginning of the year through the end of the year.

• List the Big ideas taught during that first 6 week unit and identify which are often problematic and very important for students

• Then, during the extended instructional planning time, complete the rest of the SLOT planning chart for the remainder of the school year.





SLOT Homework for May 10th

• As momentum builds for PSSA and Key Stone Exam, identify areas/topics/concepts/skills that you are noting as problematic for students during preparation activities for the assessments.

– Areas that are potential targets for SLOT strategy next year.

– Bring the list of items and when they were initially taught (e.g., September 18‐23).


Conclusion• The learning needs of struggling students and students with

disabilities in mathematics is extremely challenging for teachers.

• The research base addressing the specific instructional strategies and interventions clearly suggests the importance of Explicit Instructional Techniques1. Interleave Worked Solution Strategy‐IWSS2. Spaced Learning overtime‐SLOT3. Fluency & Automaticity4. Instructional Scaffolding Scaffolding‐Word Problems

1. Content, Task and Material Scaffolding

5. Strategies to Develop Improved Algebraic Thinking

• Conclusion‐‐‐

BRING BACK YOUR TEXT or INSTRUCTIONAL MATERIALS


QUESTIONS?


Contact Information:Paul J. [email protected]

@pjr146

MAXIMIZE ALL STUDENTS MATHEMATICAL LEARNING IN …...maximize all students’ mathematical learning...

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