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Topics for DiscussionDay 2 Summer 2014Mathematics Training
Standards for Mathematical Practice (SMP)
Differentiated Instruction
Mathematical Literacy
8:00 – 9:45 Discussion and Engagement
Activities
9:45 – 10:00 Break
10:00 - 12:00 Discussion
12:00 – 1:00
1:00 – 3:00 PLC Training with PD Team Members
Annie Fetter of Math Forum talks about "Notice" and
"Wonder"
Mathematically proficient students…
“Practices are an engine for focusing, and a reward for doing so.”
Jason ZimbaLead Writer CCSSM
“One important purpose of learning mathematics is to develop useful, analytic, quantitative, logical ways of looking at the world and thinking about things. When mathematical ways of thinking begin to become automatic – not just ways one can use, but ways one is LIKELY to use – it is reasonable to call them, habits: mathematical habits of mind.”
http://ttalgebra.edc.org/AHOM
Why Do We Need the Standards for Mathematical Practice?
“Two kinds of knowledge are needed of 21st century learners: mathematical content and mathematical practice.”
Implementation of the practices are critical to implementation of the shift of rigor. It is THROUGH the STANDARDS FOR MATHEMATICAL PRACTICE that deep conceptual content understanding, fluency and procedural skill, and application are attained.
Mathematical Practices are not learned so much through direct teaching methods, although teacher-modeling of their own use of SMP is important, but the practices develop over time for the students from rich opportunities that the teacher gives in the classroom.
Pay close attention to the verbs.
MP1 and MP6 are important in every aspect of teaching and learning mathematics. The purpose of these
standards is to build within students the sense that they can successfully “do” mathematics and build precision in their use of mathematical symbols, units, and language. These two standards are the Habits of Mind that students need to use in solving any mathematics
problem.Math Practice 1
“Make sense of problems and persevere in solving them”
http://www.insidemathematics.org/index.php/standard-1
Math Practice 6 “Attend to
precision”
http://www.insidemathematics.org/index.php/standard-6
How many triangles are in the diagram above?. What conjectures did you make about the problem in order to understand the solution?
What critical thinking skills did you use and did you collaborate with someone?
Did you hold steadfast until you had a sensible solution, and if so, what did you do to persist in finding the solution?
DecontextualizeRepresent as symbols, abstract the situation
ContextualizePause as needed to refer back to situation
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.
Reason abstractly and quantitatively.
#2: MATHEMATICALLY PROFICIENT STUDENTS …
x x x x
P
5
½ Mathematical Problem
http://commoncoretools.me/wp-content/uploads/2014/05/2014-05-06-Elaborations-6-8.pdf
http://commoncoretools.me/wp-content/uploads/2014/02/Elaborations.pdf
SMP Progression Document, Grades K-5
SMP Progression Document, Grades 6-8
http://www.louisianabelieves.com/docs/common-core-state-standards-resources/guide-math-practices-progression-grades-6-8.pdf?sfvrsn=2
Reasoning and Explaining
Math Practice 2 “Reason abstractly
and quantitatively”
http://www.insidemathematics.org/index.php/standard-2
Math Practice 3 “Construct viable
arguments and critique the reasoning of others”
http://www.insidemathematics.org/index.php/standard-3
Elaine Watson, Ed.D.watsonmath.com
Her site is used to:
• store interesting links to K – 12 math resources
• create posts about K – 12 math education
• expressing my own insights and sharing and building on the ideas of other
post links and resources that I use in my presentations and courses
she coaches K – 12 teachers and principals on best practice in mathematics education
She presents mathematics workshops to small and large groups on…
• instruction
• content
• assessment
• Common Core State Standards
The CMP, in collaboration with other groups established the CaCCSS-M Task Forces in order to collect, design, and organize resources that could be used in professional development (PD) that will strengthen teachers’ content knowledge to teach the standards:
• K-2 Number Sense and Place Value• Fractions from a Number Line Approach• Model with Mathematics • Transformational Geometry• High School Mathematical Modeling
http://caccssm.cmpso.org/home
“Mathematical modeling is the link between mathematics and the rest of the world.” (Meerschaert, M., Mathematical Modeling,Elsevier Science, 2010)
The process of beginning with a situation and gaining understanding about that situation is generally referred to as “modeling”. If the understanding comes about through the use of mathematics, the process is known as mathematical modeling.
K-8 Modeling Task ForceThe CCSS expects mathematically proficient students to
be able to apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.
In order for teachers to produce students capable of applying mathematics in the ways described above, they will need to engage students in tasks that require critical thinking and problem solving, Critical thinking and problem solving are skills that can be taught, however, in our current era of accountability, many teachers abandon the teaching of these skills in favor of test preparation.
Modeling and Using Tools
Math Practice 4 “Model with
mathematics
http://www.insidemathematics.org/index.php/standard-4
Math Practice 5 “Use appropriate
tools strategically”
http://www.insidemathematics.org/index.php/standard-5
Seeing Structure and Generalizing
Math Practice 7
“Look for and make use of structure”
http://www.insidemathematics.org/index.php/standard-7
Math Practice 8
“Look for and express regularity in repeated reasoning”
http://www.insidemathematics.org/index.php/standard-8
Math Practices 7 and 8 are two that really support students in understanding algebra.
http://commoncoretools.me/wp-content/uploads/2014/05/2014-05-06-Elaborations-6-8.pdf
http://commoncoretools.me/wp-content/uploads/2014/02/Elaborations.pdf
SMP Progression Document, Grades K-5
SMP Progression Document, Grades 6-8
http://www.louisianabelieves.com/docs/common-core-state-standards-resources/guide-math-practices-progression-grades-6-8.pdf?sfvrsn=2
http://mathpractices.edc.org/content/about-mps Explore the site and discover all that is
available for various grade levels 5 through HS, grade 10.
Have you ever KenKened?
“…a puzzle is supposed to be puzzling.”
Will ShortzNew York Times
Puzzle #19 3x3, Addition
Only
http://www.kenken.com/game
Tetsuya Miyamoto is a Japanese mathematics teacher who invented the numerical logic puzzle KenKen. The name translates to mean, "a puzzle that makes you smarter."
Miyamoto developed KenKen in 2004 to help his students improve their calculation skills, logical thinking and patience.
“Preparation for this world requires learning to approach new and unfamiliar problems with the confident “I can puzzle this out” attitude. Students need to develop a disposition to tackle problems with only the knowledge they have (or can find on their own) without a pre-learned solution method.”
PuzzlesAre Fun!
PermissionTo Think
Differentiate
Cognitively
Challenging
When the real world throws us a problem, it never asks us what chapter we’ve just
studied!
“Successful mathematical problem-solvers need both understanding and skill. To develop skill and confidence, children need practice, and a lot of it. But when the practice becomes too mechanical, children’s minds turn off—they ‘sleepwalk’ through the practice, and gain less from it.”
Teacher-Planning Toolsby: Melisa Hancock
Math Consultant, Kansas
Standards for Mathematical Practice Observation Tool
Sometimes referred to as the “Look fors” tool
Teacher Actions
Student Actions
Integrating the Standards of Mathematical Practice
Upper Elem. Grades
Fran Dickinson leads a number talk on an input/output table and graph, asking “What’s my rule?” In this clip, he harvests students’ observations about the underlying operation that yields specified outputs.
What SMPs do you see/hear evidence of?
High School
Cathy Humphreys engages her students in exploring properties of quadrilaterals. In this clip, her students into small groups to focus on specific quadrilaterals and use materials to test their observations.
Which SMPs can her students demonstrate?
“My Favorite NO” Formative
Assessment6 min.
“Graphing Linear Equations
: Full Body Style”5 min.
https://www.teachingchannel.org/videos/surface-area-lesson
http://connectedmath.msu.edu/
Connected Mathematics Project (CMP) is a complete mathematics curriculum for middle school teachers and students.
“Children’s goals and beliefs about learning are related to their mathematics performance.”
National Mathematics Advisory Panel, “Foundations for Success”, Final Report
“Whenever children believe that their efforts to learn make them “smarter”, they show greater persistence in mathematics learning. It is critical that teachers and other educational leaders should consistently help students and parents to understand that an increased emphasis on the importance of effort is related to improved mathematics performance.”
https://www.illustrative mathematics.org
Video LibraryEngage NY
http://thinkmath.edc.org/resource/ccss-mathematical-practices
Professional Development Modules
All Grade Levels
– Same
Template
http://www.learnnc.org/
http://commoncore.americaachieves.org/
The Mathematics Assessment Project has developed the Classroom Challenges to exemplify the types of activities needed to supplement traditional classroom practice and support the standards. The professional development modules are designed to help teachers with the practical and pedagogical challenges presented by these lessons.
There are 5 PD modules, all available for download.
Module 1 introduces the model of formative assessment used in the lessons, its theoretical background and practical implementation. Modules 2 and 3 look at the two types of Classroom Challenges in detail. Modules 4 and 5 explore two crucial pedagogical features of the lessons: asking probing questions and collaborative learning.
Map.mathshell.org
MODULE 4How can we ask questions that
improve thinking and reasoning?
• How is the role if the teacher when implementing the SMP different than the expected role of the past?
•What are some ways that you plan to be “intentional” in planning for the demonstration of, encouragement of, implementation of the standards for mathematical practice (SMP)?
• Can you describe similarities and differences between the expectations that are exhibited for grade level students (elementary and secondary) while involved in using a particular practice standard?
Thoughts…
