Essential Understandings About Rigorous Mathematics Instruction Developed in

Essential Understandings About Rigorous Mathematics Instruction Developed in collaboration with the MA DESE, the MA Math Support Specialists’ Network and Education Development Center, Inc.

Goals To establish a shared definition of “a rigorous mathematics experience for all students; ” To become familiar with the Standards for Mathematical Practice as the emerging national definition of “rigorous mathematics. ” Massachusetts Department of Elementary and Secondary Education 2

Turn and Talk In the last few weeks how have you used mathematics? Did the problem you were trying to solve involve several simple calculations? Was there more than one way of looking at the problem? 3 Massachusetts Department of Elementary and Secondary Education

The Conceptual, Procedural and Application Balance Conceptual Procedural Application

52 x 36 Standard Algorithm Area Model 50 1 52 x 36 312 1560 1872 30 1500 6 300 2 60 12 = 1872 Partial Product Word Problem 52 x 36 12 (6 x 2) 300 (50 x 6) 60 (30 x 2) +1500 (30 x 50) There are 36 seats in each row in Javier’s college level Computer Science class. There are 52 rows in the classroom. How many seats are there in all? 1872 Focus Coherence Clarity Rigor

Increasing the Mathematical Rigor 6 + 5 = _______ What pairs of numbers add up to 11? What pairs can you find if you don’t restrict yourself to whole numbers? How do you know you have them all? Massachusetts Department of Elementary and Secondary Education 6

Increasing the Mathematical Rigor Increasing the rigor does not necessarily mean going faster or going further ahead in the curriculum It means “going deeper” What do we mean by “going deeper? ” 7 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor What is the rule for finding the mean (or average) of a set of numbers? 8 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor Find the mean (average) of the following set of eight numbers: 4, 6, 9, 5, 13, 12, 9, 10 9 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor Find two different sets of eight numbers, each with a mean (average) of 8. 5 (The numbers don’t have to be integers. ) 10 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor The mean age of males in MA is 40. 6 and the mean age of females in MA is 36. 2. Maria says that she has a shortcut for finding the mean age of all the people in MA: “You just take the mean of 40. 6 and 36. 2. It’s 38. 4” Is she correct? Why or why not? Massachusetts Department of Elementary and Secondary Education 11

Experiencing the Rigor Working in groups of 3 Each person does task A or B Everyone do task C As a group discuss, how would you approach task D How would you rate each task in terms of rigor? Low, Medium, High Which tasks made you think? Why? Massachusetts Department of Elementary and Secondary Education 12

Increasing the Mathematical Rigor Question A How do you find the perimeter of a rectangle? What is the area formula for a rectangle? 13 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor Question B What is the area of a rectangle with a length of 7 and a width of 3? What is the perimeter? 14 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor Question C What’s the largest possible area of a rectangle that has a perimeter of 20 inches? What’s the smallest possible area? 15 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor Question D Given a rectangle with a fixed perimeter (i. e. the total perimeter is a particular length and that total length does not change), describe how the area changes as the length and width of the rectangle change. 16 Massachusetts Department of Elementary and Secondary Education

Increasing the Mathematical Rigor ≠ doing more and doing it faster heavier work load Rigor = going into greater depth conceptual understanding, procedural understanding and real world application Massachusetts Department of Elementary and Secondary Education 17

2011 MA Math Frameworks - 2 Key Parts 1) Standards for Mathematical Practice Carry across all grade levels Describe habits of mind of a mathematically proficient student 2) Standards for Mathematical Content K-8 standards presented by grade level Organized into domains that progress over several grades Grade intros give 2– 4 focal points at each grade level High school standards presented by conceptual category (Algebra and Functions, Geometric Measurement, etc. ) Massachusetts Department of Elementary and Secondary Education 18

Standards for Mathematical Practice 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. Massachusetts Department of Elementary and Secondary Education 19

What does it look like in the classroom? http: //www. americaachieves. org/issues/comm on-core-in-practice-great-teachersdemonstrate-moving-to-deeperlearning? bcpid=2324725292001&bckey=AQ~ ~, AAACGDPFg 8 k~, w 0 fem. Idt 92 JI 4 VFi 2 Xmzt 6 r w. Njjo. Nj. D&bclid=2296617881001&bctid=230545550 3001 20 Massachusetts Department of Elementary and Secondary Education

Turn and Talk As a Superintendent, what can you do to promote rigor in your schools? What assistance from DESE would help you in this effort? 21 Massachusetts Department of Elementary and Secondary Education

How we can help Share what works with urban liaisons in mathematics, science and literacy Monthly meetings- every district should have representatives Liaisons identify key focus each year Coordinate our efforts with DSAC teams and Commissioner’s liaisons Individual district assistance as requested! 22 Massachusetts Department of Elementary and Secondary Education

Grade 5 PARCC 23 Massachusetts Department of Elementary and Secondary Education

Grade 5 MCAS 24 Massachusetts Department of Elementary and Secondary Education

Grade 5 MCAS 25 Massachusetts Department of Elementary and Secondary Education

Grade 8 MCAS 26 Massachusetts Department of Elementary and Secondary Education

Grade 5 PARCC 27 Massachusetts Department of Elementary and Secondary Education