start! known to new college/career anchors and math performance
TRANSCRIPT
Agenda
1. What are College/Career Anchors?2. What are Math Performance
Standards?3. Why are they Important?4. Leading Change = Making Priorities5. Broadest Impact6. Plan for Success
Math Mathematically proficient students can…Explain meaningConjectureReason abstractlyCritique Reasoning
A Shift in Perspective
The CCSS for Mathematics compel a change in the culture of traditional mathematics classroom.
• In the typical mathematics classroom students are “too busy covering content” to be engaged with mathematics.
The CCSS attempt to tell teachers when to slow down and emphasize student understanding of significant mathematical ideas.
Cognitive Targets – CCSS Requires Focus on Rigorous Elements
NAEP 2009 PISA 2009
Locating / Recalling
Integrating / Interpreting
Critiquing / Evaluating
Accessing and retrieving
Integrating and interpreting
Reflecting and evaluating
Questions for Implementation
1. What can I affect? 2. What is most important?3. What will be most difficult, and
therefore take the most time to change?
But what does “higher standards” mean?
• More topics? – No. The U.S. curriculum is already cluttered with too
many topics
• Teaching topics in earlier grades?– No. Analyses of the standards of high-performing
countries suggest otherwise.– In Singapore, division of fractions is a 6th grade
expectation; in the U.S. it is typically a 4th or 5th grade expectation.
– In Japan, probability is introduced in the 7th grade; in the U.S., it can be found anywhere throughout grades 3-6, depending on the state.
A Shift in Perspective
Current U.S. curricula (“mile wide, inch deep”) coupled with high-stakes testing pressures teachers to
– “cover” at “pace”
– turn the page regardless of student needs
However, the study of mathematics should not be reduced to merely “a list of topics to cover”
Singapore preaches, “Teach less, learn more”
Agenda
1. What are College/Career Anchors?2. What are Math Performance
Standards?3. Why are they Important?4. Leading Change = Making Priorities5. Broadest Impact6. Plan for Success
Broad Impact The College / Career Readiness Anchors & Math Performance Standards have the Broadest Impact Across All School Personnel
• Specific and Measureable– Order a group fractions and label them on a
number line• Contain a performance verb that describes what
students will do to demonstrate achievement– Order, Label
• State the specific context in which the student will apply that performance– e.g. written, oral, short answer, presentation
Criteria for Learning Target Statements
Learning Progression
Draw a basic number line from 0 to 10
Locate simple whole
numbers on a number line
Place halves in fraction form on a number
line
Locate tenths in decimal form
on a number line
Indicate the approximate location of
thirds, fourths, and fifths on a number line
Identify and locate the
approximate location of decimals in
hundredths on a number line
Compare fractions,
decimals and mixed numbers by identifying their relative position on a number line
Standard: Identify the relative position of simple positive fractions, positive mixed numbers, and positive decimals and be able to evaluate the values based on their position on a number line.
Classifying Targets
ProductsThe ability to create tangible products, such as term papers, science fair projects, and art sculptures that meet certain standards of quality and present concrete evidence of academic proficiency.
ReasoningThe ability to use knowledge and understanding to figure things out and solve problems.
PerformanceThe development of proficiency in doing something where it is the process that is important such as playing a musical instrument, reading aloud, speaking in a second language or using psychomotor skills.
KnowledgeMastery of substantive subject content where mastery includes both knowing and understanding it.
• Identify sight words• Identify similes and metaphors• List defining characteristics of various literary
genres• Count and group concrete manipulatives by
ones, tens, and hundreds to 1,000
Knowledge Target Examples
• Make a prediction based on evidence• Distinguish between fact and opinion• Evaluate information from a variety of
resources• Classify and compare triangles by sides and
angles
Reasoning Target Examples
• Read aloud with fluency and expression• Demonstrate the use of self-correction
strategies• Find and justify the laws of exponents with
numeric bases using inductive reasoning• Model, identify and describe square, prime
and composite numbers
Performance Target Examples
• Produce a grammatically correct sentence• Develop a proper paragraph form in a written
composition• Compose a written composition using the
five-step writing process• Create a design with more than one line of
symmetry
Product Target Examples
Begin by analyzing the level of thinking required by the standard
Assess the degree of depth or complexity of knowledge reflected in the content standards and assessments
Determine how deeply a student needs to understand the content for a given response/assessment
Types of Target = Level of Thinking
Learning Goals
1. What is Cognitive Demand?2. What are the SKILLs
involved?3. How do I teach it / change
my teaching?4. What does it look it?
Assess?
A Shift in Perspective
•Too often, students view mathematics as a trivial exercise because they are rarely given the opportunity to grapple with and come to appreciate the intrinsic complexity of the mathematics.•Despite our instincts and best intentions, we need to stop “GPS-ing” our students to death.
Source: Shannon, A. (2010). Common Core: Two Perspectives on Tasks and Assessments. Presentation at the Urban Mathematics Leadership Network Retreat, June 2010.
“The Standards for Mathematical Practice
describe varieties of expertise that
mathematics educators at all levels should
seek to develop in their students. These
practices rest on important processes and
proficiencies with longstanding importance in
mathematics education.” (CCSS, 2010)
The Standards for Mathematical Practice
The Standards for Mathematical Practice
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.
The Standards for Mathematical Practice
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.
Strategic Competence
AdaptiveReasoning
ProductiveDisposition
ProceduralFluency
Conceptual Understanding
“Encouraging these practices in students of all ages should be as much a goal of the mathematics curriculum as the learning of specific content” (CCSS, 2010).
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.
The Standards for Mathematical Practice
The description of each Mathematical Practice begins with the same first three words:
Mathematically proficient students …
The Standards for Mathematical Practice
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.
The Mathematical Practices “describe the
thinking processes, habits of mind and
dispositions that students need to develop a
deep, flexible, and enduring understanding of
mathematics; in this sense they are also a
means to an end.”
The Standards for Mathematical Practice
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.
MP #1: Make sense of problems and persevere in solving them.•Mathematically proficient students … •analyze givens, constraints, relationships •and goals … they monitor and evaluate •their progress and change course if •necessary … and continually ask •themselves, “Does this make sense?”
The Standards for Mathematical Practice
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.
MP #3: Construct viable arguments and critique the reasoning of others
Consider the following subtraction algorithm: • How could I demonstrate the idea that the
algorithm always works?
400 – 139 399 – 138
43 – 17 46 – 20
Points of Intersection: Content and Practices
MP #7: Look for and make use of structure
Partitioning• 8 x 7• 33 + 58
Points of Intersection: Content and Practices
MP #7: Look for and make use of structure
Example:
Understanding and interpreting the equation of a line expressed in “Point-Slope Form”
• y – y1 = m(x – x1)
Points of Intersection: Content and Practices
First Things First
If I cannot teach in a manner which engages at the higher levels of cognitive demand, content standards do not
matter.
To Dos
1. Training = Awareness2. Direct Instruction 3. Daily Planning4. Curriculum Tagging5. Resource ID & Sharing