Focus on 2014 Content: Math Mastery

Transcription

1 Focus on 2014 Content: Math Mastery Bonnie Goonen & Susan Pittman-Shetler July 17 & 18, 2013

2 Session Objectives Identify content of the Mathematics module of the 2014 GED test Explore essential mathematical practices and behaviors Discuss beginning strategies for the classroom Identify resources that support the transition to the next generation assessment 2

3 The Magic of Algebra Think of a number and write it down. Double the number. Add 10. Divide by 2. Subtract your original number from this new number. The final number is 5. 3

4 MATHEMATICAL REASONING NEW REALITIES 4

5 Check Your Skills 5

6 What we know... People have a lovehate relationship with mathematics Twice as many people hated it as any other school subject It was also voted the most popular subject Associated Press Poll 6

7 2002 Series GED test 2014 GED test One test with two parts, one of which allowed use of calculator Content 25-30% Number Operations, Number Sense 25-30% Measurement and Geometry 25-30% Data, Statistics, and Probability 25-30% Algebra, Functions and Patterns Casio fx260-solar One test with calculator allowed on most items Content 45% - Quantitative Problem Solving Number operations Geometric thinking 55% - Algebraic Problem Solving Texas Instruments - TI 30XS Integration of mathematical practices 7

8 Mathematical Reasoning Some items require procedural skill fluency problem solving Presented in academic and workforce contexts Statistics and data interpretation standards are also included in other tests 8

9 What s new in the Mathematical Reasoning domain? Identify absolute value of a rational number Determine when a numerical expression is undefined Factor polynomial expressions Solve linear inequalities 9

10 What s new in the Mathematical Reasoning domain? Identify or graph the solution to a one variable linear inequality Solve real-world problems involving inequalities Write linear inequalities to represent context Represent or identify a function in a table or graph 10

11 What s not directly assessed on the 2014 GED Mathematical Reasoning Test? Select the appropriate operations to solve problems Relate basic arithmetic operations to one another Use estimation to solve problems and assess the reasonableness of an answer Identify and select appropriate units of metric and customary measures Read and interpret scales, meters, and gauges Compare and contrast different sets of data on the basis of measures of central tendency Recognize and use direct and indirect variation 07/

12 Then GED test Ms. Nguyen is a real estate agent. One of her clients is considering buying a house in the Silver Lakes area, where 6 houses have recently sold for the following amounts: $160,000; $150,000; $185,000; $180,000; $145,000; $190,000. What should Ms. Nguyen report as the Median price of these houses? 1) $160,000 2) $170,000 3) $180,000 4) $190,000 5) Not enough information is given. Note: Method for determining median was provided in the test booklet. 12

13 Now 2014 GED test 13

14 New Mathematical Tools 14

15 TI-30XS MultiView Calculator 15

16 It s Your Turn! "Calculators can only calculate - they cannot do mathematics." -- John A. Van de Walle ulators/scientific-calculators/ti-30xsmultiview/classroom-activities/activitiesexchange 16

17 MATHEMATICAL PRACTICES 17

18 Mathematical Practices Practices Mathematical fluency Abstracting problems Building solution pathways and lines of reasoning Furthering lines of reasoning Evaluating reasoning and solution pathways Most practices are not specific to any one particular area of mathematics content 18

19 Problem Solving In Your Classroom What opportunities do your students currently have to grapple with nonroutine complex tasks and to. reflect on their thinking and consolidate new mathematical ideas and problem solving solutions? 19

20 Solution Pathways = Problem Solving Polya s Four Steps to Problem Solving Understand the problem Look back (reflect) Devise a plan Carry out the plan Polya, George. How To Solve It, 2nd ed. (1957). Princeton University Press. 20

21 Value of Teaching with Problems Places students attention on mathematical ideas Develops mathematical power Develops students beliefs that they are capable of doing mathematics and that it makes sense Provides ongoing assessment data that can be used to make instructional decisions Allows an entry point for a wide range of students 21

22 A Few Problem-Solving Strategies Look for patterns Consider all possibilities Make an organized list Draw a picture Guess and check Write an equation Construct a table or graph Act it out Use objects Work backward Solve a simpler (or similar) problem 22

23 Let s SOLVE a Math Problem Even Albert Einstein said: Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. 23

24 SOLVE a Problem S tudy the problem (What am I trying to find?) O rganize the facts (What do I know?) L ine up a plan (What steps will I take?) V erify your plan with action (How will I carry out my plan?) E xamine the results (Does my answer make sense? If not, rework.) Always double check! 24

25 S = Study the problem What is the problem asking me to do? Find the question. We are going to practice SOLVE with this one! A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. The painter found rental costs as high as $15.00 per hour. He paid a total of $ What was the rental cost per hour? 25

26 O = Organize the Facts What facts are provided in order for you to solve the problem? Identify each fact. Eliminate unnecessary facts. List all necessary facts. A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. The painter found rental costs as high as $15.00 per hour. He paid a total of $ What was the rental cost per hour? 26

27 L = Line Up a Plan Select the operations to use. State the plan/strategy that you will use in words. I will use a multi-step approach. First, I will calculate the elapsed time that I had the steamer in number of hours. Next, I will divide the total rental amount by the number of hours I rented the steamer. This will provide me with the hourly rate. 27

28 V = Verify Your Plan 9 10 = 1 hr = 1 hr = 1 hr = 1 hr. 1 2 = 1 hr. 2 3 = 1 hr. 3 4 = 1 hr. Total 7 hrs. $28.84 / 7 = $

29 E = Examine the Results (Is it reasonable? Does it make sense? Is it accurate?) $4.12 IS reasonable because it is substantially less than the total rental amount. Also, the answer is a decimal number because the total rental amount is a decimal number. If one estimates - $28.84 is close to 28 and 7 goes into 28 four times. Therefore, the painter paid $4.12 per hour for the machine. 29

30 Let s SOLVE S O L V E 30

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33 What are the big ideas that I want students to remember days (the test) 40 months (college) 40 years (life) 33

34 Some Big Ideas in Quantitative Reasoning Number sense concepts (rational numbers, absolute value, multiples, factors, exponents) Spatial visualization Dimensions, perimeter, circumference, and area of two-dimensional figures Dimensions, surface area, and volume of threedimensional figures Interpret and create data displays Probability, ratio, percents, scale factors Graphic literacy 34

35 Some Big Ideas in Algebra Variable Symbolic Notation Equality Ratio and Proportion Pattern Generalization Equations and Inequalities Multiple Representations of Functions 35

36 Mathematics is like a video game; If you just sit and watch, You re wasting your time. 36

37 Time Out for a Video Break! 37

38 Research-Based Teaching Strategies Effective questioning Teacher responses Use of manipulatives Conceptually-based teaching 38

39 Teaching Beyond the Facts Trying to teach in the 21 st century without conceptual schema for knowledge is like trying to build a house without a blueprint. H. Lynn Erickson Concept-Based Curriculum and Instruction 39

40 Conceptual Teaching What is conceptual teaching? Using schema to organize new knowledge Developing units around concepts Providing schema based on students prior knowledge Teaching knowledge/skill/concept in context What it s not! Worksheets Drill Memorization of discrete facts 40

41 Best Practices Review Instructional Element Curriculum Design Professional Development for Teachers Recommended Practices Ensure mathematics curriculum is based on challenging content Ensure curriculum is standards based Clearly identify skills, concepts and knowledge to be mastered Ensure that the mathematics curriculum is vertically and horizontally articulated Provide professional development which focuses on: o Knowing/understandi ng standards o Using standards as a basis for instructional planning o Teaching using best practices o Multiple approaches to assessment Develop/provide instructional support materials such as curriculum maps and pacing guides and provide math coaches Technology Provide professional development on the use of instructional technology tools Provide student access to a variety of technology tools Integrate the use of technology across all mathematics curricula and courses Manipulatives Use manipulatives to develop understanding of mathematical concepts Use manipulatives to demonstrate word problems Ensure use of manipulatives is aligned with underlying math concepts Instructional Strategies Focus lessons on specific concept/skills that are standards based Differentiate instruction through flexible grouping, individualizing lessons, compacting, using tiered assignments, and varying question levels Ensure that instructional activities are learner-centered and emphasize inquiry/problem-solvi ng Use experience and prior knowledge as a basis for building new knowledge Use cooperative learning strategies and make real life connections Use scaffolding to make connections to concepts, procedures and understanding Ask probing questions which require students to justify their responses Emphasize the development of basic computational skills Assessment Ensure assessment strategies are aligned with standards/concepts being taught Evaluate both student progress/performance and teacher effectiveness Utilize student self-monitoring techniques Provide guided practice with feedback Conduct error analyses of student work Utilize both traditional and alternative assessment strategies Ensure the inclusion of diagnostic, formative and summative strategies Increase use of open-ended assessment techniques Curriculum Design Professional Development Technology Manipulatives Instructional Strategies Assessment 41

42 A Few Strategies to Get Started Model, explain, and guide Move towards self-regulation Provide opportunities for algebraic thinking Keep it real Teach often to the whole class, in small groups, and with individuals Set high expectations 42

43 High achievement always occurs in the framework of high expectation. Charles F. Kettering ( ) 43

44 QUESTIONS, INSIGHTS, SUGGESTIONS 44

45 Note: This presentation may be used and reproduced in its entirety for educational purposes in preparation for the 2014 GED test by including the following attribution text: Copyright 2013 GED Testing Service LLC. All rights reserved. Used by permission. GED and GED Testing Service are registered trademarks of the American Council on Education (ACE). They may not be used or reproduced without the express written permission of ACE or GED Testing Service. The GED and GED Testing Service brands are administered by GED Testing Service LLC under license from the American Council on Education. 45

46 Martin Kehe VP of Products, GED Testing Service Bonnie Goonen Trainer/Consultant Susan Pittman-Shetler Trainer/Consultant 46