10/29/2015
1
© 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
10/29/2015
2
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.
4
Our learning targets:
10/29/2015
3
© 2015 The College Board
5
© 2015 The College Board
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
10/29/2015
4
© 2015 The College Board
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
© 2015 The College Board
► Heart of Algebra
► Problem Solving and Data Analysis
► Passport to Advanced Math
► Additional Topics in Math
8
Four focus content domains
10/29/2015
5
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.
9
Standards of Mathematical Practice
10
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
10/29/2015
6
© 2015 The College Board
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
11
© 2015 The College Board
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).
12
10/29/2015
7
© 2015 The College Board
13
Goodbye, ACT. Hello, SAT!
© 2015 The College Board
Looking for Best-Practices inTeaching & Learning Mathematics
10/29/2015
8
© 2015 The College Board
► 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?
16
10/29/2015
9
© 2015 The College Board
Accessibility Strategies to Support Success with theRedesigned SAT/PSAT
Sameation
Differentiation
General Instructional Strategies for SAT Math
Test
Accessibility StrategiesSkill‐Building Strategies
for Math
10/29/2015
10
© 2015 The College Board
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.
19
© 2015 The College Board
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.
20
10/29/2015
11
Conceptual understanding
Concrete‐Representational‐Abstract
Color coding
Graph Paper
Graphic Organizers
Problem Solving Strategies
Metacognitive Strategies
Problem 1
10/29/2015
12
© 2015 The College Board
Heart of AlgebraSample Question (No Calculator)
23
General Instructional Strategies for SAT Math
Test
Accessibility StrategiesSkill‐Building Strategies
for Math
Small groups
Express quantities
Eliminate multiple choice answers
Ask students to create graphs and
models
Graph paper
Color coding
Problem Solving Strategies
10/29/2015
13
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.
Mayer’s 4 Cognitive Processes for Problem Solving
1.Translating (mental model)2.Integrating (using prior knowledge)3.Planning4.Executing
10/29/2015
14
+5
+5
+7
+7
Mayer’s 4 Cognitive Processes for Problem Solving
1.Translating (mental model)2.Integrating (using prior knowledge)3.Planning (decide what to do)4.Executing (do it)
10/29/2015
15
‐3
‐3
+2
+2
rise
runor
y
x
slope 3
2
© 2015 The College Board
Heart of AlgebraSample Question (No Calculator)
30
10/29/2015
16
In small groups, figure out what just happened to the line. Use quantities in
your description.
© 2015 The College Board
►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?
32
Digging Deeper
10/29/2015
17
Problem 2
© 2015 The College Board
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
34
10/29/2015
18
General Instructional Strategies for SAT Math
Test
Accessibility StrategiesSkill‐Building Strategies
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
10/29/2015
19
© 2015 The College Board
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
37
"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
$
10/29/2015
20
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
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?
40
10/29/2015
21
feet
Pounds per square inch
41
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
42
10/29/2015
22
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?
10/29/2015
24
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
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?
10/29/2015
25
© 2015 The College Board
►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?
49
Digging Deeper
Summary&Resources
10/29/2015
26
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?
51
Characterized by a familiar
• Style
• Form
• Content
Source: http://www.merriam-webster.com/dictionary/genre
Standardized Testing as a Genre
52
10/29/2015
27
► 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
53
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
54
Rich Math Tasks - Resources
10/29/2015
28
► 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
55
Rich Math Tasks - Resources
© 2015 The College Board
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.
56
10/29/2015
29
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
57
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
58
10/29/2015
30
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
59
© 2015 The College Board
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
60
10/29/2015
31
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?
61
Kathy Berry
President-ElectMichigan Council of Teachers of Mathematics (MCTM)
Coordinator of Research, Evaluation, & AssessmentMonroe County ISD
734.242.5799 x 3070
62
Your Presenters Today
Kate Fanelli
Mathematics Accessibility SpecialistMichigan’s Integrated Mathematics
Initiative (MI)2
734-451-2954