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Key Strategies for Mathematics Interventions. Interventionists Clientele. Students who may have trouble learning at the same pace as the rest of the class Students who may need alternative ways of looking at the content Students who may have learning disabilities. Professional Knowledge. - PowerPoint PPT Presentation

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Key Strategies for Mathematics InterventionsInterventionists ClienteleStudents who may have trouble learning at the same pace as the rest of the classStudents who may need alternative ways of looking at the contentStudents who may have learning disabilitiesProfessional KnowledgeTo be effective as an interventionist, you must know:Details of each CCSS (knowledge, skill, problem-solving)Learning progressions for each topicUse of diagnostic assessmentsResearch-based teaching strategiesMultiple approaches to proficiency

These are the learning goals for todays session.Intervention ProgramsTo be a good consumer, you must have the professional knowledge to judge which are adequate, and when they need to be adapted.Many are available, few are listed on the What Works Clearinghouse.See our wikiStrategies work in unisonUnderlying structure of word problemsMathematical practices: reasoning and problem-solvingVisual representationsExplicit teaching with practice, feedback and cumulative reviewUse of C-R-AMotivation An example Multi-digit addition and subtractionCCSSLearning progressionsDiagnostic assessmentsTeaching strategiesMultiple approaches

look at ccss and make notes; look at learning progressions document also6CCSSconcrete modelsdrawingsstrategies

mentally findexplain the reasoning, explain whyplace valueproperties of operationsrelationship between addition and subtraction

fluently add and subtractuse algorithmsYour interpretations:Learning Progressions1st -Joining, separating and comparing problems within 20.Demonstrate fluency within 10.Add and subtract special cases within 100.2nd -Fluently add and subtract within 20.Solve problems fluently within 100.3rd -Add and subtract within 1000 using strategies and a range of algorithms.4th -Fluently add and subtract multi-digit numbers using the standard algorithms. (up through 1,000,000)

Diagnostic AssessmentsSee the wiki

Teaching StrategiesC-R-AMental strategiesConcrete objectsVisual RepresentationsAbstract symbolic procedures (Algorithms)

Objects-Pictures-SymbolsUnderlying structure of word problemsMathematical practices: reasoning and problem-solvingVisual representationsExplicit teaching with practice, feedback and cumulative reviewUse of C-R-AMotivation 10Multi-digit ProblemsJoining, result unknownOur school has 34 fish in its aquarium. The 3rd grade class bought 15 more fish to add to the aquarium. Now how many fish are in the aquarium?Part-part-wholeThere were 28 girls and 35 boys on the playground at recess. How many children were there on the playground at recess?

Underlying structure of word problemsSeparating, result unknownPeter had 28 cookies. He ate 13 of them. How many did he have left? Write this as a number sentence: 28 13 = ____There were 53 geese in the farmers field. 38 of the geese flew away. How many geese were left in the field?Comparing two amounts (height, weight, quantity)There are 18 girls on a soccer team and 5 boys. How many more girls are there than boys on the soccer team?

See the handout of problem types.12Part-whole where a part is unknownThere are 23 players on a soccer team. 18 are girls and the rest are boys. How many boys are on the soccer team?

Distance between two points on a number line (difference in age, distance between mileposts)Misha has 34 (27) dollars. How many dollars does she have to earn to have 47 (42) dollars?

18?23

Visual representations Use the blank sheet. 13Childrens StrategiesThere were 28 girls and 35 boys on the playground at recess. How many children were there on the playground at recess?Strategies: See Handout Incrementing by tens and then ones, Combining tens and ones, Compensating.C-R-AMental strategiesConcrete objectsVisual RepresentationsAbstract symbolic procedures (Algorithms)

Objects-Pictures-SymbolsMathematical practices: reasoning and problem-solving14Number TalksA classroom method for developing understanding, skillful performance and generalization

Development of AlgorithmsThe C-R-A approach is used to develop meaning for algorithms. Without meaning, students cant generalize the algorithm to more complex problems.

Explicit teaching with practice, feedback and cumulative reviewVisual representationsRecommendation 3: Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.Strategies are BraidedRecommendation 8. Include motivational strategies in tier 2 and tier 3 interventions.Reinforce or praise students for their effort and for attending to and being engaged in the lesson.Consider rewarding student accomplishments. Allow students to chart their progress and to set goals for improvement.

Underlying structure of word problemsMathematical practices: reasoning and problem-solvingVisual representationsExplicit teaching with practice, feedback and cumulative reviewUse of C-R-AMotivation 18Alternative AlgorithmsAdding: Partial sumsSubtracting: Add ten

Multiple approaches to proficiencyPractice vs. DrillPractice usually involves word problems that draw out strategies. Students get good at using the strategies through practice. Strategies may include algorithms.Drill usually doesnt involve word problems. It is repetitive work that solidifies a students proficiency with a given strategy or procedure.Typical Learning Problems

Always start by determining what the student is doing correctly.

MultiplicationVisual representations

Multiplication C-R-AVisual representations translate to symbolic

Learning Progression

Multiplication with decimals

Multiplication with decimalsEstimate: 1.4 x 1.3 is somewhere between 1 and 2Distributive Property:1.4 x 1.3 = (1.4 x 1) + (1.4 x 0.3)1.4 x 1 = 1.41.4 x 0.3 = 1 x 0.3 + 0.4 x 0.3= 0.3 + 0.12Answer is 1.4 + 0.3 + 0.12 1.4x 1.3 0.12 0.3 0.4 1 1.82

You try it with 1.5 x 1.5. Estimate, draw, use symbolic procedure (standard algorithm)29Multiplication with Fractions

What problem does this illustrate?

Middle School ExamplesLeroy paid a total of $23.95 for a pair of pants. That included the sales tax of 6%. What was the price of the pants before the sales tax?Pretend youre the students and solve this in groups of 3. Explain your reasoning to each other. What can you explain about your own thinking that would help a struggling learner?What methods can you teach explicitly that a student might not figure out on their own?33Leroy paid a total of $23.95 for a pair of pants. That included the sales tax of 6%. What was the price of the pants before the sales tax?Label a variable: Let c = cost of the pants.Understand that 6% is not of the total cost, but 6% of the cost of the pants: 6% of c (.06)cWrite an equation: The cost of the pants c plus the sales tax (.06)c equals the TOTAL COST ___________This is where your professional judgment comes in. If you tell the student what equation to write, theyll come to depend on you to always tell them.

c.06cPoint to the drawing while you say the equation in words. This is a combination of visual representation and explicit teaching.34Create two problems similar to the previous one that allow students to transfer what theyve learned to the new problem.

Underlying structure: Join problem __ + tax = 23.95Leroy paid a total of $23.95 for a pair of pants. That included the sales tax of 6%. What was the price of the pants before the sales tax?

Division of whole numbersVisual representation: Partitioning354 photos to share among 3 children

See the CGI problem set37Partitive Division354 3(300 + 50 + 4) 3 = 100 + 10 + 1 r 21100 + 10 + 1 + 7

Measurement DivisionAlso called repeated subtractionOur class baked 225 cookies for a bake sale. We want to put them in bags with 6 in each bag. How many bags can we make?

225 60 = 165 10 bags165 60 = 105 10 bags105 60 = 55 10 bags45 30 = 15 5 bags15 12 = 3 2 bags 37 bags with 3 cookies left over

39Division with Fractions

Strategies work in unisonUnderlying structure of word problemsMathematical practices: reasoning and problem-solvingVisual representationsExplicit teaching with practice, feedback and cumulative reviewUse of C-R-AMotivation Professional KnowledgeTo be effective as an interventionist, you must know:Details of each CCSS (knowledge, skill, problem-solving)Learning progressions for each topicUse of diagnostic assessmentsResearch-based teaching strategiesMultiple approaches to proficiency