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Eric Bright 8th Grade Math Charleston Middle School [email protected]
What I’ve Learned from Three Years of Writing and Implementing Common Core Curriculum
Writing Common Core Math Curriculum
Providing personal professional development
Deep understanding of the standards
Ownership in the implementation process
Accurate assessment of student content mastery
More opportunity and higher probability for student growth
1. What wheel is required? (Get to know the Common Core)
2. How do we design a wheel like that? (Write curriculum to match CCSS)
3. How well is that wheel rolling? (Be a reflective practitioner)
Focus
Significantly narrowing the scope of content in each grade so that students achieve at higher levels and experience more deeply that which remains. “Teaching less, learning more.” – Common Core Publisher’s Criteria K-8
Teach the standards and the standards only.
Instructional Implications: Focus
Let go of “pet” projects.
Choose your rabbit trails wisely during class.
Enrichment is at grade-level, not above. (K-8 p.13)
Remediation is through grade-level standards, not below. (K-8 p.13)
Note: Much of the focus shift can be taken
care of by careful curriculum cultivation.
Assessment Implications: Focus
No above grade-level standards are assessed. (K-8 p.10)
Partial credit may be necessary to get a better picture of grade-level standard mastery.
Extra credit should probably not exist.
Coherence - Common Core Publisher’s Criteria K-8
Coherence is about making math make sense. Mathematics is not a list of disconnected tricks or mnemonics.
Vertical: It is critical to think across grades and examine the progressions in the standards to see how major content develops over time.
▪ Ex. Solving Proportions, 8 + 5 = 13 – 1 = 12 – 9 = 3
Coherence - Common Core Publisher’s Criteria K-8
Horizontal: Connections at a single grade level can be used to improve focus, by closely linking secondary topics to the major work of the grade. For example, in grade 3, bar graphs are not “just another topic to cover.” Rather, the standard about bar graphs asks students to use information presented in bar graphs to solve word problems using the four operations of arithmetic.
Instructional Implications: Coherence
Problems (not exercises) make connections wherever possible within grade-level rather than teaching in isolation. (K-8 p.13, 6b)
Relate grade-level concepts explicitly to prior knowledge. (K-8 p.13, 5c)
No micro-standards. (K-8 p.5)
Note: Much of the coherence shift can be taken
care of by careful curriculum cultivation.
Assessment Implications: Coherence
Nothing assessed for mastery out of grade-level content.
Interleaving builds coherence.
Rigor - Common Core Publisher’s Criteria K-8
To help students meet the expectations of the Standards, educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade:
▪ (1) conceptual understanding,
▪ (2) procedural skill and fluency, and
▪ (3) applications.
Rigor: Conceptual Understanding
Materials amply feature high-quality conceptual problems and questions. This includes
▪ brief conceptual problems with low computational difficulty (e.g., ‘Find a number greater than 1/5 and less than 1/4’);
▪ brief conceptual questions (e.g., ‘If the divisor does not change and the dividend increases, what happens to the quotient?’);
Rigor: Conceptual Understanding
Materials amply feature high-quality conceptual problems and questions. This includes
▪ and problems that involve identifying correspondences across different mathematical representations of quantitative relationships. (e.g., ‘How did Sara get the slope of the equation from the description?’)
▪ Ex: 8 – 5 = 3 + 7 = 10
Rigor: Procedural Skill and Fluency Manipulatives and concrete representations such as
diagrams that enhance conceptual understanding are connected to the written and symbolic methods to which they refer (see, e.g., 1.NBT).
As well, purely procedural problems and exercises are present. These include cases in which opportunistic strategies are valuable — e.g., the sum 698 + 240 or the system x + y = 1, 2x + 2y = 3 — as well as an ample number of generic cases so that students can learn and practice efficient algorithms (e.g., the sum 8767 + 2286).
Rigor: Procedural Skill and Fluency
Methods and algorithms are general and based on principles of mathematics, not mnemonics or tricks.
▪ Ex: FOIL and Proportions
Rigor: Applications Materials in grades K–8 include an ample number
of single-step and multi-step contextual problems that develop the mathematics of the grade, afford opportunities for practice, and engage students in problem solving.
Materials for grades 6–8 also include problems in which students must make their own assumptions or simplifications in order to model a situation mathematically. ▪ NOTE: May be real world or mathematical situation.
Rigor: Applications
Applications take the form of problems to be worked on individually as well as classroom activities centered on application scenarios.
Problems and activities are grade-level appropriate, with a sensible tradeoff between the sophistication of the problem and the difficulty or newness of the content knowledge the student is expected to bring to bear.
Instructional Implications: Rigor Balance CPA in classroom instruction and
homework.
Utilize both problems and exercises.
Students must make their own assumptions or simplifications in order to model a situation mathematically. (K-8 p.12)
Explicitly teach and use math vocab. (K-8, p.16)
Take advantage of cognitive disfluency, “desirable difficulties,” and productive failure.
Assessment Implications: Rigor
Formal observational formative assessments may be needed.
Summative assessments need a balance of CPA questions. (Asking students to find the error for example.)
Assessing conceptual knowledge may take discussion and/or writing.
What do we assess?
Content mastery vs. effort
Assessing at the right level
How do we assess?
Plan what mastery looks like (summative)
Plan how you will get to mastery (formative)
Lesson plans flow from assessment plans
Building an assessment with CPA
What level of rigor is the standard I’m assessing?
8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Building an assessment with CPA
8.F.1 Understand that a function is a rule that assigns to each input exactly one output.
Identify whether or not the following are functions.
Input: A circle Output: The center of that circle
Input: The center point of a circle Output: The circle around that center
Building an assessment with CPA
8.F.1 Understand that a function is a rule that assigns to each input exactly one output.
Identify whether or not the following are functions. Then explain why you think so in at least one complete sentence giving evidence specific to each problem.
Input: A circle Output: The center of that circle
Input: The center point of a circle Output: The circle around that center
A lesson is a multi-day experience that… Focuses directly on the desired standard(s) Connects explicitly to previous learning Builds the targeted level of rigor
8.F.4 Construct a function to model a linear relationship
between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Think of a lesson for the standard…
8.F.4 Determine the rate of change and initial value of the function... Interpret the rate of change and initial value… in terms of the situation it models…
Linear Weight Analysis from ISBE
Think of a lesson for the standard…
8.F.4 Determine the rate of change and initial value of the function... Interpret the rate of change and initial value… in terms of the situation it models…
Linear Weight Analysis from ISBE
Concept Procedure Application
Never say anything a student can say! Teaching is listening; learning is talking.
A lesson is a multi-day experience that…
Utilizes multiple instruction methods
▪ Whole group, small group, and individual instruction
▪ Modeling, guided learning, collaborative learning, and formative assessment
Presents concepts in varied representations
▪ Concrete, picture/graph, table, symbolic, written language, real-life situation
A lesson is a multi-day experience that… Incorporates the Math Practice Standards ▪ Make sense of problems and persevere in solving them.
▪ Reason abstractly and quantitatively.
▪ Construct viable arguments and critique the reasoning of others.
▪ Model with mathematics.
▪ Use appropriate tools strategically.
▪ Attend to precision.
▪ Look for and make use of structure.
▪ Look for and express regularity in repeated reasoning.
Being a reflective practitioner How well did a lesson encourage student content
mastery? ▪ Write it down!
How well did an assessment measure student content mastery? ▪ Data analysis
“There is no growth without reflection.”
1. What wheel is required? (Get to know the Common Core)
2. How do we design a wheel like that? (Write curriculum to match CCSS)
3. How well is that wheel rolling? (Be a reflective practitioner)
Providing personal professional development
Deep understanding of the standards
Ownership in the implementation process
Accurate assessment of student content mastery
More opportunity and higher probability for student growth
