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Implementing the NYS P-12 Common Core Learning Standards for Mathematics
Turn-Key Training GuideThis turn-key training guide was developed to assist Network Teams, Principals and Teacher Leaders in the delivery of the Power Point presentation Implementing NYS P-12 Common Core Learning Standards for Mathematics created by Margaret Brady, Teri Calabrese-Gray, and Andrew Chen. This presentation may be delivered in one sitting (approximately four hours in length) or it may be broken down into smaller segments as time permits.
Please note that slides that are marked with the symbol as slides that require the support of a mathematics specialist in the
delivery of the content, as they require deep mathematical knowledge and understanding.
The presentation contains links to videos and websites that will assist the presenter in demonstrating application of the Mathematical Shifts of the Common Core State Standards. These videos and websites can be accessed by double clicking on the hyperlinks on the slides.
May 15, 2012 1
Table of ContentsSlides 1 - 4 – The Common Core Learning Standards……………………………………………………..……………Pg 4-5
The Common Core State Standards Why Common Core Standards?
Slides 5-19 – CCSS? How they were developed and who was involved?……………………….…………………Pg 5-12
The Mathematical Standards – Who developed them? The underlying framework and the need for change. A sense of urgency What the research says
Slides 20-22 – Introduction to the Instructional Shifts ………………………………………………………………....Pg 12
Focus Coherence Fluency Deep Understanding Application Dual Intensity
Slides 23-26 – Shift 1: Focus……………………………………………………………………………………………….Pg 13-14
The power of the eraser Prioritized concepts
Slides 27-39 – Shift 2: Coherence…………………………….…………………………………………………………..Pg 14-18
The Structure is the Standards Knowing and Teaching Elementary Mathematics
May 15, 2012 2
Slides 40-44 – Shift 3: Fluency…………………………….……………………………………………………………...Pg 18-19
Key Fluencies Building on required fluencies
Slides 45-47 – Shift 4: Deep Understanding………………….………………………………………………………….Pg 19
Deep conceptual understanding
Applying to new situations
Slides 48-49 – Shift 5: Application……………………….…………………………………………………………..……...Pg 20
Provide opportunities at all grade levels to apply math concepts in “real world” situations
Slides 50-53 – Shift 6: Dual Intensity………………….…………………………………………………………..…….Pg 20-21
Practicing and understanding
Slides 54 – The Mathematical Shifts and the Standards They Require…………………………………………..….Pg 22
Conceptual Understanding, Procedural Fluency and Problem Solving Greater focus and better coherence
Slides 55 – 57 – Assessment of Learning: The Next Shift………………………………………………………………Pg 22
NYS Common Core Curriculum Modules PARCC Assessments
Slides 58 - 63 – Resources…………………………………………………………………………………………….……Pg 22-23
NYSED Mathematics Toolkit EngageNY.org The Tri-State Rubric for Mathematics NYS CCLS for Mathematics Modules Video Exemplars
May 15, 2012 3
References………………………..……………………….…………………………………………………………..…….Pg 24-31
Mathematics Toolkit – Presenter Notes & Directions for PowerPoint Presentation.
Slide # Presenter Notes Hyperlinks Slide Timing
1 Presenter Notes: This PowerPoint toolkit provides a brief history on the Common Core State Standards (CCSS) for Mathematics, the rationale behind the development of the CCSS, and an overview of the six instructional shifts needed to effectively implement the NYS P-12 CCLS for Mathematics.
Presenter Directions: Throughout the Power Point there are a number of hyperlinks (identified in bright blue lettering) that can be accessed by right clicking to “open hyperlink.” These movies, resources and activities can be used to support the various topics addressed in this presentation
Hyperlink: http://www.engageny.org
2 minutes
2 Presenter Notes: This slide provides information of how and when the CCSS conversation began and the two organizations that oversaw the development of the Common Core State Standards (CCSS).
Hyperlink:http://corestandards.org/ This is link to the National Common Core Standards website where information can be found about the
5 minutes
May 15, 2012 4
Presenter Directions: Open the hyperlink and show participants where the Common Core Mathematics Standards are found. Review them briefly.
development of the standards and all of the Common Core Standards in PDF format
3 Presenter Notes: “Why Common Core State Standards?”
Presenter Directions: Pose this question to your audience and engage in a conversation (do not advance to the next slide or you may choose to hide the next slide of the PPT).
What to Expect: Discussion usually focuses on College and Career Readiness (CCR), global competition, states would be able to compare themselves to others states for the first time, equity for all students regardless of zip code, and focus and coherence (reduce “the mile wide, inch deep” curriculum in the United States).
5 minutesfor totalactivity
Slide # Presenter Notes Hyperlinks Slide Timing
4 Presenter Notes: This slide lists rationale as to why states agreed to collaborate and develop the CCSS.
2 minutes
5 Presenter Notes: The hyperlink contained is this slide is a video that explains the process on the development of the CCSS for Mathematics. Bill McCallum and Jason Zimba, two of the principal writers, share how they worked as a team with 60 writers and various professional organizations to develop the mathematics standards. There are many other Hunt Institute videos on You Tube.
Presenter Directions: Click on the hyperlink in the title to view a video.
Hyperlink:http://www.youtube.com/watch?v=dnjbwJdcPjE The Hunt InstituteThe Mathematics Standards: How They Were Developed and Who Was Involvedby Bill McCallum, PhD, Math Team Coordinator and Jason Zimba, PhD, Math Team Coordinator
Video Timing = 8:11
10 minutes
6 Presenter Notes: Adding It Up provides a historical perspective in mathematics education and the presenter can refer participants to this
Hyperlink: Visit http://www.nap.edu/catalog.php?
2 minutes
May 15, 2012 5
document for advancing their own knowledge about how students in pre-K through 8th grade learn mathematics and it recommends how teaching, curricula, and teacher education should change to improve mathematics learning and teaching.
record_id=9822 1 to read Adding It Up online, free of cost.
7 Presenter Notes: This matter is URGENT! Presenter Directions: Emphasize that Improving K-12 Mathematics Education is an urgent matter!
10 seconds
Slide # Presenter Notes Hyperlinks Slide Timing
8 Presenter Notes: “What is the current state of mathematical performance?”Presenter Directions: The key questions for this activity are outlined on this slide
Pose these questions one at a time Ask participants to discuss at their tables. Another option is
to ask tables to count off by fours and discuss one of the four questions and report out.
Continue to the next slide and present the data
6-8 Minutes
9 Presenter Notes: This slide highlights the TIMMS study.
Presenter Directions: Ask participants if they are familiar with this study. Review the information contained on the slide and refer participants to the hyperlink for more information about this important study.
Hyperlink: http://nces.ed.gov/timss/
The Trends in International Mathematics and Science Study (TIMSS) provides reliable and timely data on the mathematics and science achievement of U.S. 4th- and 8th-grade students compared to that of students in other countries. TIMSS data have
1 minute
May 15, 2012 6
been collected in 1995, 1999, 2003, and 2007. In 2011, more than 60 countries and jurisdictions, including the United States, participated in TIMSS. More than 20,000 students in more than 1,000 schools across the United States took the assessment in spring 2011, joining almost 500,000 other students around the world taking part in TIMSS.
Slide # Presenter Notes Hyperlinks Slide Timing
10 Presenter Notes: The 2007 Trends in International Mathematics and Science Study (TIMSS) is the fourth administration since 1995 of this international comparison. Developed and implemented at the international level by the International Association for the Evaluation of Educational Achievement (IEA)—an international organization of national research institutions and governmental research agencies—TIMSS is used to measure over time the mathematics and science knowledge and skills of fourth- and eighth-graders. This report focuses on the performance of U.S. students relative to that of their peers in other countries in 2007, and on changes in mathematics and science achievement since 1995. Thirty-six countries or educational jurisdictions participated at grade four in 2007, while 48 participated at grade eight. This report also describes additional details about the achievement of U.S. student subpopulations. All differences described in this report are statistically significant at the .05 level. No statistical adjustments to account for multiple comparisons were used.
Hyperlink: http://nces.ed.gov/pubs2009/2009001.pdf
8th Grade Math
6-8 minutes
May 15, 2012 7
Note: This is 8th grade math data.Key findings from the report include the following:• In 2007, the average mathematics scores of both U.S. fourth-graders (529) and eighth-graders (508) were higher than the TIMSS scale average (500 at both grades). The average U.S. fourth-grade mathematics score was higher than those of students in 23 of the 35 other countries, lower than those in 8 countries (all located in Asia or Europe), and not measurably different from those in the remaining 4 countries. At eighth grade, the averageU.S. mathematics score was higher than those of students in 37 of the 47 other countries, lower than those in 5 countries (all of them located in Asia), and not measurably different from those in the other 5 countries.• Compared to 1995, the average mathematics scores for both U.S.
(Slide 10 continued)fourth- and eighth-grade students were higher in 2007. At fourth grade, the U.S. average score in 2007 was 529, 11 points higher than the 1995 average of 518. At eighth grade, the U.S. average mathematics score in 2007 was 508, 16 points higher than the 1995 average of 492.• In 2007, 10 percent of U.S. fourth-graders and 6 percent of U.S. eighth-graders scored at or above the advanced international benchmark in mathematics. At grade four, seven countries had higher percentages of students performing at or above the advanced international mathematics benchmark than the United States:Singapore, Hong Kong SAR, Chinese Taipei, Japan, Kazakhstan, England, and the Russian Federation. Fourth-graders in these seven countries were also found to outperform U.S. fourth-graders, on average, on the overall mathematics scale. At grade eight, a slightly different set of seven countries had higher percentages of students performing at or above the advanced mathematics benchmark than the United States: Chinese, Taipei, Korea, Singapore, Hong Kong SAR,
May 15, 2012 8
Japan, Hungary, and the Russian Federation. These seven countries include the five countries that had higher average overall mathematics scores than the United States, as well as Hungary and the Russian Federation.
Slide # Presenter Notes Hyperlinks Slide Timing
11 Presenter Notes: Does this give us cause for alarm? 10 seconds
12 Presenter Notes: PISA All students take pencil-and-paper tests, with assessments lasting a total of two hours for each student. For the PISA 2009 assessment, some participating countries/economies have also opted for an assessment of the reading of electronic texts.
Presenter Directions: The link is given for reference –
Hyperlink: http://www.oecd.org/dataoecd/1/63/34002454.pdf
PISA ( Programme for International Student Assessment)
30 seconds
13 Presenter Notes: Please note that this is math data comparing 15 year olds. Take an interactive version of the tests online at http://www.oecd.org/dataoecd/47/23/41943106.pdf
You can also consult the publication 'Take the Test ‘which lists all the publicly released items from the first three assessments (PISA 2000, 2003 and 2006).
Hyperlink: Take the Testhttp://www.oecd.org/dataoecd/47/23/41943106.pdf
PISA ( Programme for International Student Assessment)
2-3 minutes
May 15, 2012 9
The PISA test is a very rigorous test for 15 year olds and focused on mathematical application.
Slide # Presenter Notes Hyperlinks Slide Timing
14 Presenter Notes: Only 4 percent of students in the combined Organization for Economic Cooperation and Development (OECD) area, but more than 8 per cent in Belgium, Japan, Korea and the partner country Hong Kong-China – can perform the highly complex tasks required to reach Level 6.
• About a third of OECD students can perform relatively difficult tasks at Levels 4, 5 or 6, but over 49 percent of students in Finland, Korea and the partner country Hong Kong-China can perform at least at Level 4.
• About three-quarters of OECD students can perform at least mathematical tasks at Level 2 (shown above the central line in the graph). However, over a quarter of students are not proficient beyond Level 1 in Italy and Portugal, over a third in Greece and over half in Mexico and Turkey. A number of partner countries also have high numbers at Level 1 or below.
Hyperlink: First Results from PISA 2003 Executive Summary
http://www.oecd.org/dataoecd/1/63/34002454.pdf
2 minutes
May 15, 2012 10
• Eleven percent of students in OECD countries are not capable even of Level1 tasks. These students may still be able to perform basic mathematical operations, but were unable to utilize mathematical skills in a given situation, as required by the easiest PISA tasks. In some countries, over 20 percent are in this category
Presenter Directions: Spend time explaining the seven levels (above and below) so that participants can understanding and compare high and low performing countries.
Slide # Presenter Notes Hyperlinks Slide Timing
15 Presenter Notes: In 2006, the average U.S. score in mathematics literacy was 474, lower than the OECD average score of 498. Thirty-one jurisdictions (23 OECD jurisdictions and 8 non-OECD jurisdictions) scored higher, on average, than the United States in mathematics literacy in 2006. In contrast, 20 jurisdictions (4 OECD jurisdictions and 16 non-OECD jurisdictions) scored lower than the United States in mathematics literacy in 2006. When comparing the performance of the highest achieving students—those at the 90th percentile—U.S. students scored lower (593) than the OECD average (615) on the mathematics literacy scale. Twenty-nine jurisdictions (23 OECD jurisdictions and 6 non-OECD jurisdictions) had students at the 90th percentile with higher scores than the United States on the mathematics literacy scale.
1 minutes
16 Presenter Notes: The red bar represents some of our leading states. This graph shows the percentage of students achieving at an advanced level and how various states performed on the PISA 2006 in
30 seconds
May 15, 2012 11
comparison to other states and countries. Even our best states (Massachusetts) performed considerably lower than the leading countries. The cutting edge defines a country’s ability to remain competitive.
17 Presenter Notes: The National Assessment of Educational Progress (NAEP) is the largest nationally representative and continuing assessment of what America's students know and can do in various subject areas. Assessments are conducted periodically in mathematics, reading, science, writing, the arts, civics, economics, geography, and U.S. history. In 2011, New York State is the only state whose 4th graders scored lower than in 2009.
Hyperlink: http://nces.ed.gov/nationsreportcard/ National Assessment of Educational Progress (NAEP)
30 seconds
Slide # Presenter Notes Hyperlinks Slide Timing
18 Presenter Notes: This slide depicts the 4th grade NAEP Math Results. Presenter Directions: Review these results with participants
2 minutes
19 Presenter Notes: This slide depicts the 4th grade NAEP Math Results. Presenter Directions: Review these results with participants
2 minutes
20 Presenter Notes: This 14-minute video provides an overview of the Common Core State Standards in Mathematics. NYS Commissioner of Education John B. King Jr. and contributing author David Coleman discuss the background of the Common Core State Standards, their value in the state, the principles of their development, and the changes required of schools during this transition. Based on the video where there any “ah-ha” moments for you? Presenter Directions: Determine need/time to view during the presentation. The viewing of this video could be assigned as a pre-session assignment.
Hyperlink: Common Core Math EngageNY.orghttp://engageny.org/resource/common-core-in-mathematics-overview/
15 minutes (if viewing complete video)
May 15, 2012 12
21 Presenter Notes: There are six instructional shifts necessary to implement the NYS P-12 New York State P-12 Common Core Learning Standards for Mathematics.
5 seconds
22 Presenter Notes: The six shifts represent key areas of focus as teachers and administrators work to implement the NYS P-12 New York State P-12 Common Core Learning Standards for Mathematics. Educators are likely to be at different stages in practicing these shifts, however, focusing on these areas can help schools and districts develop a common understanding of what is needed in mathematics instruction as they move forward with implementation. Presenter Directions: Ask participants to read the shifts, think about what the shifts mean, and what would these look like in a mathematics classroom?
2 minutes
Slide # Presenter Notes Hyperlinks Slide Timing
23Presenter Notes: Ask participants to read the shift, think about what the shift means, and what it would look like in a mathematics classroom.
3-4 minutes
24 Presenter Notes: Ask participants to paraphrase the shift. Focus involves depth, not breadth. The intent of the NYS P-12 New York State P-12 Common Core Learning Standards for Mathematics is to use the power of the eraser and get rid of a curriculum that is “a mile wide and an inch deep.” Another key word in the definition is “prioritized”. Educators need to be sure they are spending more time on those concepts critical to mathematical proficiency. Students need to have deep conceptual understanding to be able to transfer skills across concepts and grades.
3-4 minutes
25 Presenter Notes: The purpose of the National Center for Education Statistics' Kids' Zone is to provide information to help visitors learn about schools; decide on a college; find a public library; engage in several games, quizzes and skill building about math, probability, graphing, and
Hyperlink: Dare to Compare http://nces.ed.gov/nceskids/eyk/?flash=true Sample TIMMS questions
5 -8 minutes (problem and discussion)
May 15, 2012 13
mathematicians; and to learn many interesting facts about education. Of course, all of these things have been designed to be fun too, so jump in! Dare to Compare, a part of the Kids’ Zone website, contains questions from the Trends in International Mathematics and Science Study (TIMSS), the Civic Education Study (CivEd) and National Assessment of Education Progress (NAEP).
Presenter Directions: Ask participants to engage in a math problem on the Dare to Compare site and discuss possible application in the mathematics classroom.You could use the math questions on the Dare to Compare site as “Do Nows” or Bell Ringers, peer to peer, learning centers, and quizzes for students to work on in teams or pairs, review, or share with parents in your newsletter.
Slide # Presenter Notes Hyperlinks Slide Timing
26 Presenter Notes: • First-year college remediation problem: Mismatch of
definitions of College Readiness between higher education and K-12
• [Teachers should] teach to greater mastery of fewer topics vs. covering more
• [Teachers need to] build a solid foundation for students in early grades on key topics
• Solid foundation in early grades enables greater success later
Hyperlink:http://www.youtube.com/watch?v=2rje1NOgHWs&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=18&feature=plcp
The Hunt Institute The Importance of Focus in Mathematics by Bill McCallum, PhD, Math Team Coordinator and Jason Zimba, PhD, Math Team Coordinator
Video Timing = 2:42
5 minutes
27 Presenter Notes: (Shift 2 Coherence) Ask participants to read the shift, think about what the shift means, and what it would look like in a mathematics classroom.
1 minute
28 Presenter Notes: Ask participants to paraphrase the shift. Instead of treating math in each grade as a series of disconnected topics,
3-4 minutes
May 15, 2012 14
principals and teachers insure coherence by carefully connecting the learning within and across grades so that, for example, fractions or multiplication develop across grade levels and students can build new understanding onto foundations built in previous years. Each standard is not a new event, but an extension of previous learning.
Slide # Presenter Notes Hyperlinks Slide Timing
29 Presenter Notes: Bill McCallum, one of the authors of the CCSS, discusses the importance of coherence and how we should instill in students an understanding why it all fits together (mathematics is not a subject that keeps branching out – it is based on underlying principles that help mathematics come together under one umbrella).
Hyperlink: http://www.youtube.com/watch?v=83Ieur9qy5k&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=17&feature=plcpThe Hunt Institute The Importance of Coherence in Mathematics by Bill McCallum, PhD, Math Team CoordinatorVideo Timing = 4:38
6- 8 minutes
30 Presenter Notes: The article, The Structure is the Standards, was posted in the winter of 2012 on Bill McCallum’s blog and written by Bill McCallum, Phil Daro and Jason Zimba. The article allows for powerful conversations around the CCSS and the philosophy behind the development of those standards.
Presenter Directions: Distribute copies of the entire article (only two pages); The Structure is the Standards to participants. Prior to asking participants to read the article, advance to the next slide.
Hyperlink: http://commoncoretools.me/2012/02/16/the-structure-is-the-standards/
The Structure is the Standards by Phil Daro Senior Fellow America’s Choice & Pearson, Bill McCallum, PhD, Math Team Coordinator and Jason Zimba, PhD, Math Team Coordinator.
2-3 minutes
May 15, 2012 15
31 Presenter Directions: As participants to engage in mathematical discussion and answer the questions on the slide with an elbow partner after reading the article. Select participants to report out to the group.
12-15 minutes
32
Presenter Notes: The example that follows is from the book “Knowing and Teaching Elementary Mathematics” by Liping Ma. This book is a must read for mathematics educators. The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.Usually the answer to this question is procedural and the response is, “multiply by the reciprocal.” Others share a mnemonic device, such as “keep, switch, flip.”
1 minute
Slide # Presenter Notes Hyperlinks Slide Timing
33
Presenter Notes: At your tables, discuss with others how they would present this problem to students. This is just an opportunity to discuss possible solutions that will be shared later. (The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.)
2-3 minutes
34
Presenter Notes: What is the most common phrase we hear teachers say when teaching students to divide fractions?Presenter Directions: (The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.) The most common phrase is to invert and multiply. Ask them to tell you why this works. Do they have a deep conceptual understanding themselves?
30 seconds
Presenter Notes: Based on the responses of Chinese teachers, we 10 seconds
May 15, 2012 16
35
need to start using the same language and focus on multiplication being the inverse of division. Presenter Notes: (The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.) Discuss vocabulary terms: division, number, multiplication, equivalent, and reciprocal
36
Presenter Notes: (Extend) “dividing by a number is equivalent to multiplying by its reciprocal.” (The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.)
10 seconds
Slide # Presenter Notes Hyperlinks Slide Timing
37
Presenter Directions Ask each table to come up with as many ways to solve/model this problem as possible. Provide them plenty of time to complete the task. Most will start out with the typical solutions/models, but the more time they have, the more creative they become using various supplies at their tables. Examples could include (how many halves are in one and three-quarters?): a number line, measuring cups, manipulatives (i.e., candy, money, Legos, fraction bars etc.)
(The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.)
*Use chart paper to chart responses – have participants do a gallery walk so they can see multiple solutions.
15 – 20 minutes
May 15, 2012 17
38
Presenter Notes: Ask the participants to determine which method they used (as outlined above) to represent the problem. Be specific (Measurement, Partitive, or Factors and Product) to ensure that participants are using content specific vocabulary. (The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.)
2-3 Minutes
Slide # Presenter Notes Hyperlinks Slide Timing
39
Presenter Notes: Presenter poses question: What does it take to understand division of fractions? This concept map lists all the concepts students need to understand in order to solve the problem presented. This shows the importance of coherence required within and across grades. (The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.)
1-2 minutes
40 Presenter Notes: Ask participants to read the shift, think about what the shift means, and what it would look like in a mathematics classroom.
1 minute
41 Presenter Notes: Ask participants to paraphrase the shift. Students 3-4
May 15, 2012 18
must have the skill to carry out procedures flexibly, accurately, efficiently and appropriately. Ask participants how they can assist with fluency, even if they are not the classroom teacher? Who else inside and outside the school can help with fluency in your district/school? Share ideas - physical education teachers, music teachers, cafeteria staff and other support personnel, parents, family members, day care providers (parents drop off their children prior to the start of school or they go there after school until the parent finishes work), local libraries and other after school providers/organizations.
minutes
42 Presenter Notes: Granny Prix is a fun activity for students to work on fluency
Presenter Directions: Demonstrate how Granny Prix can be used in a classroom as a tool to helping students become more fluent.
Hyperlink: Granny Prix http://www.multiplication.com/flashgames/GrannyPrix.htm
3-4 minutes
Slide # Presenter Notes Hyperlinks Slide Timing
43 Presenter Notes: Create school and classroom contests around the fluencies; make these a fun school project
2 minutes
44 Presenter Notes: We must strike a balance between the two. Each grade has one or two fluencies teachers should focus on.
Presenter Directions: Click on the hyperlink in the title. Bill McCallum and Jason Zimba, explain the importance of fluency but not at the expense of conceptual understanding
Hyperlink: The Hunt Institute Mathematical Fluency: A Balanced Approach by Bill McCallum and Jason Zimbahttp://www.youtube.com/watch?v=ZFUAV00bTwA. . Video Timing = 1:57
3 minutes
45 Presenter Notes: Ask participants to read the shift, think about what the shift means, and what it would look like in a mathematics classroom. Students with conceptual understanding know more than isolated facts and methods - they understand why a mathematical idea is important and the contexts in which it is useful.
1 minute
May 15, 2012 19
46 Presenter Directions: Ask participants to paraphrase the shift. Presenter Notes: Teachers take time to understand not only the content standards, but the Standards for Mathematical Practice describe the student expertise needed to develop a deep conceptual understanding of mathematics.
3-4 minutes
47
Presenter Directions: Present this problem to the group. Ask them to work on the problem and then be prepared to share a justification. This leads to a great discussion and demonstrates how students could determine if this could possibly be true through collection of data. (The presenter may want to seek assistance from a mathematics content specialist if the presenter is not familiar or comfortable with the mathematical content.)
6-8 minutes
Slide # Presenter Notes Hyperlinks Slide Timing
48 Presenter Directions: Ask participants to read the shift, think about what the shift means, and what it would look like in a mathematics classroom. Focus on some of the key vocabulary. Identify opportunities for students to apply math concepts in “real world” situations.Presenter Notes: The process of modeling that includes choosing and using appropriate mathematics and statistics to analyze and understand situations, is key in improving decisions as well as linking classroom mathematics and statistics to everyday life, work, and decision-making.
1 minute
49 Presenter Directions: Ask participants to paraphrase the shift. Presenter Notes: Students are expected to use math and choose the appropriate mathematical models even when they are not prompted to do so.
3-4 minutes
May 15, 2012 20
50 Presenter Directions: Ask participants to read the shift, think about what the shift means, and what it would look like in a mathematics classroom. Presenter Notes: Teachers struggle on balancing how much time they spend on procedural skills and the amount of time they are spending on deep conceptual understanding/application. They must find that balance. Students need to practice and understand mathematics.
1 minute
51 Presenter Directions: Ask participants to paraphrase the shift. Presenter Notes: Teachers create opportunities for students to participate in authentic practice and make use of those skills through extended application of math concepts.
3-4 minute
Slide # Presenter Notes Hyperlinks Slide Timing
52 Presenter Directions: This video is 2:38 (total) Click on the hyperlink and play the video. Pause at 1:00 when the contestant asks to poll the audience.
Presenter Notes: Ask participants: “To answer this question, what mathematics does the contestant need to know? (Chart the responses). Then say: “Now that you know this, can you now solve the problem?”
Hyperlink:http://www.youtube.com/watch?v=BbX44YSsQ2I
When Not Knowing Math Can Cost You $15,000
Video Timing = 2:38
3 minutes
May 15, 2012 21
53 Presenter Directions: Discuss the necessary vocabulary and why square numbers are called square numbers. List the square numbers (1x1=1, 2x2=4, 3x3=9, 4x4=16, 5x5=25, etc.). Now ask them to solve the problem. Continue the video from where it was paused. Discuss the shifts addressed in the problem and provide specifics.
Hyperlink:http://www.youtube.com/watch?v=BbX44YSsQ2I
When Not Knowing Math Can Cost You $15,000
Video Timing = 2:38
3 minutes
Slide # Presenter Notes Hyperlinks Slide Timing
54 Presenter Directions: Click on the hyperlink in the title. Presenter Notes: Jason Zimba solidifies the need for the shifts and how educators need to focus on these shifts to help all students be college and career ready.
Hyperlink: http://www.youtube.com/watch?v=5pBOnvzC_Yw&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=29&feature=plcp
The Hunt InstituteThe Mathematics Standards and the Shifts They Require by Bill McCallum and Jason Zimba, PhD, Math Team CoordinatorVideo Timing = 1:15
2-3 minutes
55 Presenter Notes: What’s Next? 10 seconds56 Presenter Notes: New York State Assessment Transition Timeline –
review of the planned assessments.3-4 minutes
May 15, 2012 22
57 Presenter Notes: Assessments in relation to the Common Core Shifts 2-3 minutes
58 Presenter Notes: Use this toolkit to support your work. 3-4 minutes
59 Presenter Notes: There are also resources available on EngageNY.org Bookmark it on your desktop and visit it often for updates.
30 seconds
60 Presenter Notes: Collaborations between New York State and other states have resulted in the creation of additional tools and resources. The Tri-State Rubric Quality Review Rubric for Mathematics produced by a collaboration between New York State, Rhode Island and Massachusetts is available currently on EngageNY.org
1 minute
Slide # Presenter Notes Hyperlinks Slide Timing
61 Presenter Notes: New York State is due to release Mathematics Curriculum Modules in July of 2012. Week long intensive professional development sessions are planned for teachers, leaders, principals and BOCES Network Teams to learn how to roll out these modules in classrooms beginning in September of 2012.
2 minutes
62 Presenter Notes: New York State is also in the process of developing more than 500 videos to support quality teaching and learning. The first videos will be available in July of 2012.
20 seconds
63 Presenter Notes: Questions?
May 15, 2012 23
References
Askey, R. (1999, Fall). Knowing and Teaching Elementary Mathematics. American Educator, 1-8. Retrieved from http://mit.edu/
6.969/ www/ readings/ ma-review.pdf
Common Core State Standards Initiative. (2011). Common Core State Standards. Retrieved from http://www.corestandards.org/
This is link to the National Common Core Standards website where information can be found about the development of the
standards and it contains all of the Common Core Standards in PDF format.
Daro, P., McCallum, B., & Zimba, J. (2012, February 16). The Structure is the Standards [Web log post]. Retrieved from
http://commoncoretools.me/ 2012/ 02/ 16/ the-structure-is-the-standards/
May 15, 2012 24
The article, The Structure is the Standards, was posted in the winter of 2012 on Bill McCallum’s blog and written by Bill
McCallum, Phil Daro and Jason Zimba. The article allows for powerful conversations around the CCSS and the philosophy
behind the development of those standards.
Ericsurf6. (2007, October 5). The World’s Easiest Math Puzzle [Video file]. Retrieved from http://www.youtube.com/ watch?
v=WHtAmNhDFMY
This is a fun mathematics activity for students in grades 5 -12.
Gonzales, P. (2009). Highlights from TIMSS 2007: Mathematics and Science Achievement of U.S. Fourth and Eighth-Grade Students
in an International Context. Retrieved from National Center for Education Statistics website: http://nces.ed.gov/
pubs2009/ 2009001.pdf
The 2007 Trends in International Mathematics and Science Study (TIMSS) is the fourth administration since 1995 of this
international comparison. Developed and implemented at the international level by the International Association for the
Evaluation of Educational Achievement (IEA)—an international organization of national research institutions and
governmental research agencies—TIMSS is used to measure over time the mathematics and science knowledge and skills
of fourth- and eighth-graders. This report focuses on the performance of U.S. students relative to that of their peers in other
countries in 2007, and on changes in mathematics and science achievement since 1995. Thirty-six countries or educational
jurisdictions participated at grade four in 2007, while 48 participated at grade eight. This report also describes additional
May 15, 2012 25
details about the achievement of U.S. student subpopulations. All differences described in this report are statistically
significant at the .05 level. No statistical adjustments to account for multiple comparisons were used.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it Up: Helping Children Learn Mathematics. Washington, DC:
National Academies Press.
Adding It Up provides a historical perspective in mathematics education and the presenter can refer participants to this
document for advancing their own knowledge about how students in pre-K through 8th grade learn mathematics and it
recommends how teaching, curricula, and teacher education should change to improve mathematics learning and teaching.
Ma, L. (1999). Studies in Mathematical Thinking and Learning: Knowing and Teaching Elementary Mathematics: Teachers’
Understanding of Fundamental Mathematics in China and the United States (A. H. Schoenfeld, Ed.). Hillsdale, NJ: Lawrence
Erlbaum Associates.
Ma, L. (2010). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China
and the United States (Studies in Mathematical Thinking and Learning Series) (2nd ed.). Routledge.
Mathclips. (2007, July 26). When Not Knowing Math Can Cost You $15,000 [Video file]. Retrieved from http://www.youtube.com/
watch?v=BbX44YSsQ2I
This video clip from the popular television game show, “Who Wants to Be a Millionaire” demonstrates mathematical
application in a real world situation.
May 15, 2012 26
McCallum, B. (2011). Mathematic Standards: How They Were Developed and Who Was Involved [Video file]. Retrieved from
http://www.youtube.com/ watch?v=dnjbwJdcPjE
The hyperlink contained is this slide is a video that explains the process on the development of the CCSS for Mathematics.
Bill McCallum and Jason Zimba, two of the principal writers, share how they worked as a team with 60 writers and various
professional organizations to develop the mathematics standards.
McCallum, B., & Zimba, J. (n.d.). Mathematical Fluency: A Balance Approach [Video file]. Retrieved from http://www.youtube.com/
watch?v=ZFUAV00bTwA.
Bill McCallum and Jason Zimba, explain the importance of fluency but not at the expense of conceptual understanding
National Center for Education Statistics. (n.d.). National Assessment of Educational Progress (NAEP). Retrieved from U.S.
Department of Education website: http://nces.ed.gov/ nationsreportcard/
The National Assessment of Educational Progress (NAEP) is the largest nationally representative and continuing
assessment of what America’s students know and can do in various subject areas. Assessments are conducted periodically
in mathematics, reading, science, writing, the arts, civics, economics, geography, and U.S. history. In 2011, New York
State is the only state whose 4th graders scored lower than in 2009.
NCES Kids’ Zone. (n.d.). Dare to Compare. Retrieved from U.S. Department of Education website: http://nces.ed.gov/ nceskids/ eyk/ ?
flash=true
May 15, 2012 27
The purpose of the National Center for Education Statistics’ Kids’ Zone is to provide information to help visitors learn
about schools; decide on a college; find a public library; engage in several games, quizzes and skill building about math,
probability, graphing, and mathematicians; and to learn many interesting facts about education. Of course, all of these
things have been designed to be fun too, so jump in! Dare to Compare, a part of the Kids’ Zone website, contains questions
from the Trends in International Mathematics and Science Study (TIMSS), the Civic Education Study (CivEd) and National
Assessment of Education Progress (NAEP).
New York State Education Department. (2011). Common Core in Mathematics: Overview. Retrieved from http://engageny.org/
resource/ common-core-in-mathematics-overview/
This 14-minute video provides an overview of the Common Core State Standards in Mathematics. NYS Commissioner of
Education John B. King Jr. and contributing author David Coleman discuss the background of the Common Core State
Standards, their value in the state, the principles of their development, and the changes required of schools during this
transition.
New York State Education Department. (2011). EngageNY. Retrieved from http://engageny.org/
New York State’s Race to the Top initiative resource page. This site contains resources relating to Common Core State
Standards, Data Driven Instruction and Principal and Teacher Leader Evaluation. It was designed by New York State
specifically for teachers, principals and network teams.
May 15, 2012 28
Oliver, N. (n.d.). Diaper Derby [Math Game]. Retrieved from Fun 4 the Brain website: http://www.multiplication.com/ flashgames/
DiaperDerby.htm
Diaper Derby is a fun activity for students to work on fluency
Oliver, N. (n.d.). Granny Prix [Math Game]. Retrieved from multiplication.com website: http://www.multiplication.com/ flashgames/
GrannyPrix.htm
Granny Prix is a fun activity for students to work on fluency
Programme for International Student Assessment. (n.d.). First Results from PISA 2003 [Executive Summary]. Retrieved from
Organisation for Economic Co-operation and Development website: http://www.oecd.org/ dataoecd/ 1/ 63/ 34002454.pdf
The PISA test is a very rigorous test for 15 year olds and focused on mathematical application. You can also consult the
publication ‘Take the Test ‘which lists all the publicly released items from the first three assessments (PISA 2000, 2003 and
2006).
Programme for International Student Assessment (PISA). (n.d.). Retrieved from Organisation for Economic Co-operation and
Development website: http://www.oecd.org/ document/ 61/ 0,3746,en_32252351_32235731_46567613_1_1_1_1,00.html
May 15, 2012 29
PISA All students take pencil-and-paper tests, with assessments lasting a total of two hours for each student. For the PISA
2009 assessment, some participating countries/ economies have also opted for an assessment of the reading of electronic
texts.
Trends in International Mathematics and Science Study (TIMSS). (n.d.). Retrieved from Institute of Educational Science website:
http://nces.ed.gov/timss/
The Trends in International Mathematics and Science Study (TIMSS) provides reliable and timely data on the mathematics
and science achievement of U.S. 4th- and 8th-grade students compared to that of students in other countries. TIMSS data
have been collected in 1995, 1999, 2003, and 2007. In 2011, more than 60 countries and jurisdictions, including the United
States, participated in TIMSS. More than 20,000 students in more than 1,000 schools across the United States took the
assessment in spring 2011, joining almost 500,000 other students around the world taking part in TIMSS.
Wu, H.-H. (2012, January 1). Teaching Geometry According to the Common Core Standards. Retrieved from University of California
website: http://math.berkeley.edu/ ~wu/
Zimba, J. (n.d.). The Mathematics Standards and the Shifts They Require [Video file]. Retrieved from http://www.youtube.com/
watch?v=5pBOnvzC_Yw&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=29&feature=plcp
Jason Zimba solidifies the need for the shifts and how educators need to focus on these shifts to help all students be college
and career ready.
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Zimba, J., & McCallum, B. (n.d.). The Importance of Focus in Mathematics [Video file]. Retrieved from http://www.youtube.com/
watch?v=2rje1NOgHWs&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=18&feature=plcp
This Hunt Institute video created by Jason Zimba and Bill McCallum, writers of the Common Core Mathematics Standards,
discusses the Mathematics shift of Focus.
Zimba, J., & McCallum, B. (n.d.). Mathematical Fluency: A Balance Approach [Video file]. Retrieved from
http://www.youtube.com/ watch?v=ZFUAV00bTwA&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=27&feature=plcp
Bill McCallum and Jason Zimba, explain the importance of fluency but not at the expense of conceptual understanding
Zimba, J., & McCallum, W. (n.d.). The Importance of Coherence in Mathematics [Video file]. Retrieved from
http://www.youtube.com/ watch?v=2rje1NOgHWs&feature=autoplay&list=UUF0pa3nE3aZAfBMT8pqM5PA&playnext=1
Bill McCallum, one of the authors of the CCSS, discusses the importance of coherence and how we should instill in
students an understanding why it all fits together (mathematics is not a subject that keeps branching out – it is based on
underlying principles that help mathematics come together under one umbrella).
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