success strategies for the math sat/psat -...

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© 2015 The College Board

Success Strategies for the Math SAT/PSAT

MASSP Principals Summit – November 2, 2015Kathy Berry

MCTM President-ElectCoordinator of Research, Evaluation,

and Assessment, Monroe County ISDKate Fanelli

Mathematics Accessibility SpecialistMichigan’s Integrated Mathematics Initiative (MI)2

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Brought to you as a collaborative project by:

► I CAN compare the mathematics portions of the SAT/PSAT and the ACT.

► I CAN begin to recognize and apply the eight Standards for Mathematical Practice in the SAT/PSAT questions.

► I CAN begin to understand how accessibility strategies can support ALL learners in demonstrating mathematics understanding on the SAT/PSAT.

► I CAN begin to identify “look-fors” around best-practices in teaching and learning mathematics.

► I CAN begin to plan strategies for addressing SAT/PSAT performance in my school’s mathematics classes/courses.

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Our learning targets:

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SAT ACT38 w/calculator; 20 non‐calculator; 58 total

ProblemCount

60, calculator permitted on all

45 multiple choice; 13 “student response” (gridded)

ProblemTypes

All multiple choice, 4 choices

55 minutes w/calculator; 25 minutes non‐calculator; 80 minutes total in two sessions

Timing 60 minutes, one test session

No penalty Errors Penalty, ¼ point each wrong response

CAS calculators permitted except on non‐calculator part

Calculator* Non‐CAS calculators only

Deliberate contexts of science, social studies; tables/graphs in reading

Ties to other Subjects

None specified

Rich mathematics classes with problem solving & modeling

Preparation Classwork plus “tips and tricks”

SAT Math vs. ACT Math

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SAT ACT

Heart of Algebra (33%) Pre‐Algebra (20% ‐ 25%)

Problem Solving & Data Analysis (29%) Elementary Algebra (15% ‐ 20%)

Passport to Advanced Math (28%) Intermediate Algebra (15% ‐ 20%)

Additional Topics in Math (10%) Coordinate Geometry (15% ‐ 20%)

Standards of Mathematical Practice:Interwoven

Plane Geometry (20% ‐ 25%)

Trigonometry (5% ‐ 10%)

“…to support excellent instruction by designing assessments that measure the skills that matter most for college and career readiness.”Module 1 Facilitator’s Guide, Redesigned SAT

PURPOSE “The ACT mathematics test is a 60‐question, 60‐minute test designed to

assess the mathematical skills students have typically acquired in courses taken

up to the beginning of grade 12.” –http://www.actstudent.org/testprep/descriptions/

mathcontent.html

SAT Math vs. ACT Math - CONTENT


► Heart of Algebra

► Problem Solving and Data Analysis

► Passport to Advanced Math

► Additional Topics in Math

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Four focus content domains

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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.

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Standards of Mathematical Practice

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Assessing the Standards of Mathematical Practice

“The test covers all mathematical practices, with an emphasis on problem solving [1], modeling [4], using appropriate tools strategically [5], and looking for and making use of structure [7] to do algebra. The practices emphasized in the Redesigned SAT are central to the demands of postsecondary work. Problem solving requires students to make sense of problems and persevere to solve them, a skill highly rated by postsecondary instructors (Conley et al., Reaching the Goal, 2011). Modeling stresses applications characteristic of the entire postsecondary curriculum. Students will be asked throughout high school, college, and careers to make choices about which tools to use in solving problems. Finally, structure is fundamental to algebra and to other more advanced mathematics.”

- Redesigned SAT Test Specifications Document, p. 133

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Calculator and No-Calculator Portions► The Calculator portion:

- gives insight into students’ capacity to use appropriate tools strategically.

- includes more complex modeling and reasoning questions to allow students to make computations more efficiently.

- includes questions in which the calculator could be a deterrent to expedience.

• students who make use of structure or their ability to reason will reach the solution more rapidly than students who get bogged down using a calculator.

► The No-Calculator portion:

- allows the redesigned SAT to assess fluencies valued by postsecondary instructors and includes conceptual questions for which a calculator will not be helpful.

► Which calculators are acceptable to use? You might be surprised! (KB)

https://sat.collegeboard.org/register/calculator-policy

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How Does The Math Test Relate to Instruction in Science, Social Studies, and Career-Related Courses?

► Math questions contribute to Cross-Test Scores, which will include a score for Analysis in Science and Analysis in History/Social Studies. The Math Test will have eight questions that contribute to each of these Cross-Test Scores.

- Question content, tables, graphs, and data on the Math Test will relate to topics in science, social studies, and career.

► On the Reading Test and Writing and Language Test, students will be asked to analyze data, graphs, and tables (no mathematical computation required).

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Goodbye, ACT. Hello, SAT!


Looking for Best-Practices inTeaching & Learning Mathematics

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► Your “look-for” – identify the VERBS

► What are students doing?

► What are teachers doing?

► Your “look-for” – identify the NOUNS

► What is it that students will be thinking about, working with?

► What is it that teachers will be thinking about, working with?

► Scale of 1 (Starting out) to 5 (We’ve got this nailed!):

► Students

► Math teachers

SMPs & Best-Practices

From the College Board itself:

“The most important thing students can do to prepare for the SAT is to take the most challenging courses available to them, do their best work, and benefit from daily instruction that prepares them for college and career.

The single best way teachers can prepare students is to continue to develop and focus on the college and career readiness skills they are already teaching in their discipline.”

Source: The Redesigned SAT Professional Development Module 1, Facilitator’s Guide, page/slide 36.

What is the best preparation for performing well on the rSAT/rPSAT?

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Accessibility Strategies to Support Success with theRedesigned SAT/PSAT

Sameation

Differentiation

General Instructional Strategies for SAT Math

Test

Accessibility StrategiesSkill‐Building Strategies

for Math

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General InstructionalStrategies for SAT Math Test► Ensure that students practice solving multi-step problems.

► Organize students into small working groups. Ask them to discuss how to arrive at solutions.

► Assign students math problems or create classroom-based assessments that do not allow the use of a calculator.

► Encourage students to express quantitative relationships in meaningful words and sentences to support their arguments and conjectures.

► Instead of choosing a correct answer from a list of options, ask students to solve problems and enter their answers in grids provided on an answer sheet on your classroom and common assessments.

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Skill-Building Strategies for Math► Provide students with explanations and/or equations that incorrectly describe a

graph and ask them to correct the errors.

► Ask students to create pictures, tables, graphs, lists, models, and/or verbal expressions to interpret text and/or data to help them arrive at a solution.

► Organize students in small groups and have them work together to solve problems.

► Use “Guess and Check” to explore different ways to solve a problem when other strategies for solving are not obvious.

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Conceptual understanding

Concrete‐Representational‐Abstract

Color coding

Graph Paper

Graphic Organizers

Problem Solving Strategies

Metacognitive Strategies

Problem 1

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Heart of AlgebraSample Question (No Calculator)

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Test


for Math

Small groups

Express quantities

Eliminate multiple choice answers

Ask students to create graphs and

models

Graph paper

Color coding

Problem Solving Strategies

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Process Definition Knowledge

TranslatingConverting sentence

into mental representation

Semantic and linguistic

IntegratingBuilding a mental model of the problem situation

Schematic

PlanningDevising a plan for how to solve the problem

Strategic

Executing Carrying out the plan Procedural

Mayer’s 4 Cognitive Processes for Problem Solving

Royer, James M. Mathematical Cognition. Greenwich, Conn.: Information Age Pub., 2003. Print.


1.Translating (mental model)2.Integrating (using prior knowledge)3.Planning4.Executing

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+5

+5

+7

+7


1.Translating (mental model)2.Integrating (using prior knowledge)3.Planning (decide what to do)4.Executing (do it)

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‐3

‐3

+2

+2

rise

runor

y

x

slope 3

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Heart of AlgebraSample Question (No Calculator)

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In small groups, figure out what just happened to the line. Use quantities in

your description.


►What strategy and tools did we use to approach this problem?

►Why might a teacher choose these?

►What other strategies and tools might other participants (or students) use?

►Which Standards of Mathematical Practice might be applicable to this problem, and why?

►What classroom “look-fors” might you expect to see when these strategies are being used?

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Digging Deeper

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Problem 2


Heart of Algebra (Calculator)When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

A) p = 0.44d + 0.77

B) p = 0.44d + 14.74

C) p = 2.2d – 1.1

D) p = 2.2d – 9.9

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Test


for Math

Multi‐step problems

No calculator

Use pictures and graphs

Work in small groups

Graphic organizer

CRA

Think aloud(metacognitive strategies)

Prototype for Lesson Construction

Touchable Visual

Discussion:Makes sense

of concept

1

2

Learn to record these ideas

V. Faulkner and DPI Task Force adapted from Griffin

Symbols

Simply record keeping!

Mathematical Structure

Discussion of the concrete

Quantity

Concrete display of concept

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Heart of Algebra (Calculator)When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

A) p = 0.44d + 0.77

B) p = 0.44d + 14.74

C) p = 2.2d – 1.1

D) p = 2.2d – 9.9

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"Confed‐Cup 2005 ‐ Laolawelle" by Florian K ‐ Own work. Licensed under CC BY‐SA 3.0 via Wikimedia Commons ‐https://commons.wikimedia.org/wiki/File:Confed‐Cup_2005_‐_Laolawelle.JPG#/media/File:Confed‐Cup_2005_‐_Laolawelle.JPG

$

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Touchable Visual


of concept

1

2



Symbols




Quantity


When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of dfeet below the surface?

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feet

Pounds per square inch

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For every 5 feet, psi increases by 2.2I can see

there’s a y‐intercept greater than 0, and it’s around 15.

feet

Pounds per square inch

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When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure pin pounds per square inch at a depth of d feet below the surface?

A) p = 0.44d + 0.77 B) p = 0.44d + 14.74 C) p = 2.2d – 1.1 D) p = 2.2d – 9.9

Just knowing those two things, which of these answers is looking good?

Why are some 0.44 and some

2.2?

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http://mathequalslove.blogspot.com/2012/11/new‐ymxb‐foldable.html

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Touchable Visual


of concept

1

2



Symbols




Quantity


When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure pin pounds per square inch at a depth of d feet below the surface?

A) p = 0.44d + 0.77 B) p = 0.44d + 14.74 C) p = 2.2d – 1.1 D) p = 2.2d – 9.9

I definitely think it’s B because of the intercept.

Is it possible that .44 is right?

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►What strategy and tools did we use to approach this problem?

►Why might a teacher choose these?

►What other strategies and tools might other participants (or students) use?

►Which Standards of Mathematical Practice might be applicable to this problem, and why?

►What classroom “look fors” might you expect to see when these strategies are being used?

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Digging Deeper

Summary&Resources

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High-quality teaching and learningof the Michigan career and college readiness mathematics standards,

including the Standards of Mathematical Practice (SMP)

through

Engaging in rich math tasks which develop and use conceptual understanding and the ability to apply mathematics understanding and skills

Engaging in worthwhile opportunities to practice skills to attain fluency

Engaging in frequent formative assessment with descriptive feedback used by students for improvement and for tracking their own growth

Developing key life-long mathematical habits of mind as illustrated in the eight Standards of Mathematical Practice

Throughout their K-12 mathematics experience – not just during high school

What does all that mean for Mathematics Preparation?

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Characterized by a familiar

• Style

• Form

• Content

Source: http://www.merriam-webster.com/dictionary/genre

Standardized Testing as a Genre

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► MAP – Mathematics Assessment Project

► http://map.mathshell.org/

► Check out the Lessons, Tasks, and Tests tabs

► FREE

► EMATHS – Embracing Mathematics, Assessment, & Technology in High Schools

► http://www.emathsmi.com/resources.php

► Michigan project led by Macomb ISD

► Many FREE resources (units of study and tasks)

► Training (excellent!) may yet be offered

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Rich Math Tasks - Resources

► MAISA Math Units

► https://gomaisa-public.rubiconatlas.org/Atlas/Public/View/Default

► FREE

► Check with your ISD/RESA/RESD/AESA for upcoming training events

► All units have a formative assessment task and at least one highlight lesson with rich tasks that promote mathematical discourse, multiple representations, and/or multiple solution strategies

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► Algebra for All (Algebra4All)

► http://a4a.learnport.org/

► Michigan statewide project - Check out Lesson Sharing and Resources - FREE

► Some A4A documents are housed under the PRIME menu option

► On-line professional learning courses are still available through Michigan Learnport

► Project PRIME – Promoting Reform In Mathematics Education

► http://a4a.learnport.org/page/14-15-prime-year-4

► Michigan statewide project from the Michigan Mathematics and Science Centers Network (MMSCN) – View PRIME resources under the PRIME tab - FREE

► Training may yet be offered around the state

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Practice with Khan Academy► The College Board and Khan Academy have partnered to

provide online SAT® test preparation programs and resources entirely free of charge.

► On June 2, 2015, Khan Academy released an interactive and personalized practice program for the redesigned SAT.

► Features include:- Thousands of practice problems- Personalized tutorials on test content- Official SAT practice questions and full-length tests- Comprehensive reporting for students - Access anytime, anywhere — for free

► The College Board is working with educators, community groups, college access organizations, and parents to provide the necessary resources to propel students to college success.

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Practice with Khan Academy► Practice programs will be individually targeted to address each student’s greatest

areas of need (based on diagnostic assessment on khanacademy.org.).

► Khan Academy provides online guides and suggestions to help teachers use Khan Academy supports in classroom instruction.

► www.khanacademy.org/sat - Overview with David (College Board) and Sal (KA)

► https://www.youtube.com/watch?v=QvLS9pP65sA - Overview of SAT, PSAT practice and tutorials available through Khan Academy

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Resources for Teachers

SAT Teacher Implementation Guide

https://collegereadiness.collegeboard.org/pdf/redesigned-sat-k12-teacher-implementation-guide.pdf

Why you want a copy: Full details in teacher-friendly form on the 4 major math domains on the rSATAdditional examplesPlanning toolsTools to use with students

Test Specifications for the Redesigned SAT®https://collegereadiness.collegeboard.org/pdf/test-specifications-redesigned-sat.pdf

Why you want a copy:Even more detail about the rSATMore sample questions

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More Resources for TeachersCollege Board Website

https://collegereadiness.collegeboard.org/

Michigan & SAT Website

https://collegereadiness.collegeboard.org/state-partnerships/michigan?excmpid=MTG308-AL-1-mat

Sample redesigned test questions

https://collegereadiness.collegeboard.org/sample-questions

Sample redesigned PSAT Practice Test

https://collegereadiness.collegeboard.org/sites/default/files/psat_nmsqt_practice_test_1.pdf

Sample redesigned SAT Practice Tests

https://collegereadiness.collegeboard.org/sat/practice/full-length-practice-tests

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What’s in the SAT Teacher Implementation Guide?► Information and strategies for teachers in all subject areas

► Overview of SAT content and structure

► Test highlights

► General Instructional Strategies

► Sample test questions and annotations

- Skill-Building Strategies for your classroom

- Keys to the SAT (information pertaining to the redesigned SAT structure and format)

- Rubrics and sample essays

► Scores and reporting

► Advice to share with students

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Thinking Forward► What might I want to do NOW to inform

my staff, students, and parents about the mathematics portion of the SAT, PSAT?

► What might I want to consider doing within the next 6-24 months to better help staff and students with the mathematics portion of the SAT, PSAT?

► What are some mathematics teaching and learning “look-fors” which would tell me we are on the right track for student preparedness for the SAT/PSAT?

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Kathy Berry

President-ElectMichigan Council of Teachers of Mathematics (MCTM)

Coordinator of Research, Evaluation, & AssessmentMonroe County ISD

[email protected]

734.242.5799 x 3070

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Your Presenters Today

Kate Fanelli

Mathematics Accessibility SpecialistMichigan’s Integrated Mathematics

Initiative (MI)2

[email protected]

734-451-2954

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