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Billings Public SchoolsBillings Public SchoolsDeveloping Standards-Based Education Developing Standards-Based Education
System: A Look at Standards-Based System: A Look at Standards-Based Instruction in Elementary, Middle and Instruction in Elementary, Middle and
High School ClassroomsHigh School Classrooms
The State of Montana Mathematics Education Forum
September 21-22, 2009 Helena, MT
Presenters:Presenters:
• Lisa Scott, 9-12 Curriculum & K-12 Assessment• Courtney Niemeyer, K-6 Mathematics Coach• Angel Zickefoose, K-6 Mathematics Coach• Kim Komar, Middle School Math Teacher• Linda Horst, Middle School Math Teacher• Lisa Wood, High School Math Teacher
Lisa Scott
9-12 Curriculum & K-12 Assessment
Billings Public Schools Billings Public Schools District K-12 Mathematics District K-12 Mathematics Curriculum DevelopmentCurriculum Development
• District Demographics• District Goal • SEC used to connect
Curriculum, Instruction, Professional Development and Assessment
Assessment PDInstructio
n
Curriculum
What Content Will Be Taught?
• Began With Rewriting K-6 Mathematics Curriculum– Vertical and Horizontal Alignment
• Middle School Examined Current Reality– State Standards, Enacted Curriculum, and State CRT
Assessment– Asked hard questions – Challenging conversations
• High School Examined Alignment of Intended, Enacted and Assessed Curriculum– Discussions about alignment
SEC Map ActivitySEC Map Activity
• Take a few minutes to examine and discuss the contour maps
• Discuss the alignment of the four maps.• Do you see any noticeable patterns?• Describe the similarities and differences
between the maps?• What conclusions can you make?• What content topics and/or cognitive levels
would you suggest improving?
7
2005 Comparison – Standards, Instruction, and CRT
Identified Curriculum Identified Curriculum PointsPoints
• 7th & 8th Coarse Grain Maps the Same– Needed to examine Fine Grain Maps
• Shift Emphasis• Build Trust• District Learning Objectives• Resources
– Primary and supplemental• Technology
MS Algebra Teachers
Geometry Teachers
Algebra Teachers
12th – MathStandards
10th CRTMath - 2005
Professional Development Professional Development DecisionsDecisions
• Elementary Math Coaches• MS & HS Primary Resource & Technology Training• MS & HS Summer Courses and Curriculum Work• Middle School Math Professional Learning Communities• Middle School Math Coach• Senior High School becomes a member of the Successful
Practics Network• High School elimination of Pre-Algebra• High School developed and wrote the curriculum for Algebra
Foundations• Algebra Foundation PLC
Assessment
• District Survey of Enacted Curriculum (SEC)• State CRT Assessments• District NWEA Assessments• District Essential Skills Assessments• New District Primary Report Cards
Courtney Niemeyer
K-6 Mathematics Coach
What Content Should Be Taught?
How Will I Teach It?
How Will I Know Students Learned It?
How Will I Know Students Have Learned It?
Angel Zickefoose
K-8 Mathematics Coach
What Content Should Be What Content Should Be Taught?Taught?
• Essential Learner Outcomes– Taken from District Curriculum– 8 to 10 standards per quarter – Taught to mastery for ALL students– Other curriculum items are taught, but to a different
level– Intervention focused on ELO’s– Vertically aligned – Intermediate Math team
Essential Learner OutcomesBlack – 1st Q; Green – 2nd Q; Red = 3rd Q
Read, write, order and compare numbers to 10,000
Compare and order whole numbers through millions
Read, write, model, order and compare to 1,000,000
Read number words less than 10,000 and write corresponding numeric value
Write standard and expanded forms to 1,000,000
Round numbers to the nearest 1000 using numbers up to 10,000
Round whole numbers to 1,000,000
Model, recognize and generate forms of decimals to hundredths
Model, recognize and generate forms of decimals to thousandths
Read and write decimals
Apply commutative and associative property of addition, and multiplication and identity property of addition and multiplication
Apply commutative and associative property of addition and multiplication
Commutative and Associative Properties of Addition & Multiplication
How will I teach it?
• Coaching Cycle • Observation Form with feedback • Re-teach opportunities
How will I know students have learned it?
• Common Formative Assessments• Summative Assessments
Our Journey
School A School B School C School D
Staff Buy-In No No Yes Yes
Principal Buy-In
No Yes No Yes
Math Through Inquiry Project is funded through an ESEA Title II Part B Mathematics and Science Partnership Grant awarded by the Montana Office of Public Education.
Kim Komar
Middle School Mathematics Teacher
What Content Should Be Taught?What Content Should Be Taught?
– Billings School District 2 provided time for teachers to align the district curriculum to the Montana State Standards.
– Each summer the district has curriculum meetings that allows teachers to revise and edit the curriculum and pacing guides.
– As a PLC group, we have developed learning targets for each chapter or unit.
Student Learning Target SheetStudent Learning Target Sheet
Learning Target EvidenceReady (Y or N) Right
Why? Lucky Guess
or Understand Wrong
Why? Simple Mistake or
More Study
1I understand good mathematical justifications and can give justifications for a statement about numbers.
2 I can use conventions for multiplication and division.
3I can substitute values for a letter and find the solutions.
4I understand the number properties and can apply them.
5I can use letters in the formulas for the area and perimeter of rectangles.
6 I understand the distributive property.
7I can make a table of a situation and express relationships in terms of letters.
8 I can graph situations.
9 I can solve problems in a systematic way.
Student Learning TargetsStudent Learning Targets
– Learning targets are given to the students at the beginning if each chapter or unit
– Learning targets are placed on the board for daily reference
– Learning targets are used to create common assessments
How Will I Teach It?How Will I Teach It?
• Collaborate with teachers in the PLC– Develop Targets– Create Assessments– Lesson Plan Together– Share Results– Marzano’s classroom strategies guide daily
instructional practices– Believe that all students can learn!
How Will I Know Students How Will I Know Students Learned It?Learned It?
• Formative Assessments– Activities– Note taking– Homework-allow students to correct or redo
assignments– Quick Quizzes– Observing and reviewing student work– Individual instruction– Whole class discussions, small group discussions,
and partner discussions– Guided practice – white boards, paper, Elmo– Common Assessments – allowing students to correct
or redo their assessments
How Will I Know Students How Will I Know Students Learned It?Learned It?
• Self and Peer Assessment– Make corrections and redo assignments
– Peer share and compare groups (2 to 4 students)
– Students use the learning targets to monitor their progress before and after assessments
Grade Scoring Scale for Assessments
4Student answers all parts of the question correctly and shows good justification.
3Student has good justification, sets the problems up correctly, but has a minor error.
2Student has the problem set up correctly, but has errors and a poor justification.
1Student has some of the problem correctly set up, but has major errors and poor justification.
0 Student has nothing correct, major error, and no justification.
A = 3.25 – 4.00 B = 2.50 – 3.24 C = 2.00 – 2.49 D = 1.50 – 1.99 F = Below 1.50
Linda Horst
Middle School Mathematics Teacher
What Content Will Be Taught?
• District Level Curriculum: o Centered on Standards
•
• NCTM standards prior to adoption of the Montana standards and benchmarks
• Blended with Montana benchmarks • Major revision in 2004• Yearly revisits
What Content Will Be Taught?
• Curriculum adds focus to daily planningo Provides Focus at a state, local and building level o Allows Flexibility
•
• Pacing Guideso Provides continuity between classrooms and within
the district grade leveled schoolso Encourages inclusion of all standards and
benchmarks
How Will I Teach?Weekly Planning:• Using curriculum & pacing
guides develop continuum from prior to future lesson
• Sharing ideas/concerns with teaching partner
• Select activities and materials based on the goals and objectives of the week
• Goals included on weekly assignment board
• Students include lessons and topic of study in weekly planner
Daily Relevance:
• Daily Activity Board• Review of daily topic/goals at
beginning of class• Revisit goals as teaching
progresses• Focus on builing connections
between standards/benchmarks
• Closure... Where were we today? What's our next learning opportunity?
How Will I Know Students Have Learned?
• Formative Assessmentso Student Involvement
Assignment completion Class Discussion Partner conversations Excitement about mathematics
o Guided Practice Successeso Quick Quizzeso Thoroughness of student justifications both verbal and
written
How Will I Know Students Have Learned?
• Summative Assessmentso Homework Quizo Section Quizo Chapter Assessmento State Assessment Results
• Othero Students' willingness to attempt more rigorous
problem setso Students' ability to maintain and extend the application
of learned concepso Feedback from former students
And Equally Important:How Will My Students Know They Have Learned
• Confident verbalization of mathematical process• Use of mathematical vocabulary• Increased involvement in partner, group and class discussion• Self-checking of solutions• Self-Grading of homework• Willingness to share justifications
o Divergent thinking with common solutiono Questioning of and celebrating other problem solving
methods• Self-revision of Errors• Less reliance on calculators • Increasing comfort level when facing rigorous new concepts• And yes . . . better grades and test scores
Montana Standards: Guiding our students' future...
"We are attempting to educate students today so that they will be ready to solve future problems that have not yet been identified, using technology not yet invented, based on scientific knowledge not yet discovered." J.J. Lagowski
15 Minute BreakRefreshments in the
Lounge
Lisa Wood
High School Mathematics Teacher
What Content Should Be Taught?
SEC – Teacher completed the Survey and as a district we looked at
the maps.– Maps gave a nice picture as to where taught the material well
and where we had holes– Took a look at the middle school maps and noticed that many
times we were reteaching what they had already taught.– Had to learn to trust the teachers before us and when looking a
prerequisites to what we were teaching understand that we didn’t need to reteach them, but review them quickly and get on to what was important for that class.
– This helped free up time for covering new material better.
What Content Should Be Taught?
Pacing Guides– At the district level, during the summers, teachers aligned our
current books to both the district and state standards.– Teachers trusted previous teachers and did not reteach
material.– The pacing guides allowed for individual teacher differences
and built an appropriate time line for teaching the material. Certain sections were eliminated, some were built up and some were moved to cover what the standards said we should cover.
– The new ELE’s that the state is developing will be a much needed aid to districts following this plan.
How Will We Teach It?
Algebra Foundations– Class used to support the Algebra course.– Curriculum written by Billings teachers– Revisits the Standards, Objectives, Goals that are
deemed important for Algebra to better help students to understand the material. This class is more application based.
How Will We Teach It?
Senior– Teachers are utilizing the Pacing Guide.– Standards, Goals, Objectives are written on the board at the
beginning of each class period so students are aware of the standards that are being addressed.
– Math teachers have a common lunch period if want to collaborate.
– Technology– Smart Board – 75 in building, 20 of which were provided by
parents.
– Certified instructor at Senior to help teacher become familiar with the technology.
How Will We Teach It?
Successful Practices Network– http://www.successfulpractices.org– Rigor/Relevance Framework– Gold Seal Lessons
• Instructional Focus – National Standards in all curriculums, not just math
• Student Learning – What the students learn.• Performance Tasks – An overview of the lesson and a description of
what both the teacher and the students will do to accomplish the task.• Essential Skills – What will be accomplished.• Scoring Guide – A scoring rubric is provided.
– Teachers writing their own Gold Seal Lessons– Over 40 written at Senior at this point.– Small Group meetings to facilitate relationships among staff and
support each other in the process.
How Will I Teach It?How Will I Teach It?
LevelsLevels
CC DD
AA BB 1 2 3 4 5
456
321
Bloom’sBloom’s
ApplicationApplication
Rigor & Relevance Framework
654321
A B
D
1 2 3 4 5Application
C
Knowledge
GOLDSEAL
LESSONFitting a Model to Data
SubjectMath
Rigor/RelevanceFramework
Grade Level 9
Instructional Focus
Number Operations and Concepts: Students use number, number sense, and number relationships in a problem-solving situation. Students communicate the reasoning used in solving these problems.Algebraic Concepts and Relationships: Students use algebraic methods to investigate, model, and interpret patterns and functions involving numbers, shapes, data, and graphs in a problem-solving situation. Students evaluate and communicate the reasoning used in solving these problems.Statistics and Probability: Students use statistics and probability to analyze given situations and the results of experiments. Students communicate the reasoning used in arriving at a conclusion.Tools and Technology: Students use the appropriate tools and technologies to model, measure, and apply the results in a problem-solving situation. Students communicate the reasoning used in solving these problems.Problem-Solving and Mathematical Reasoning: Students apply a variety of problem-solving strategies to investigate and solve problems from across the curriculum as well as from practical applications.
Student Learning
Students will collect and organize data using a table and a scatter plot to determine which graph (linear, quadratic, or exponential) will best model the data.Students will develop a presentation to share their findings and data with peers.
Performance Task
Overview:Students will be given information about a business such as a pizza parlor and its number of pizzas sold and its total sales. They will make a table with the data and create a scatter plot and describe any patterns that they see. Students will collect and organize data using a table and scatter plot. They will model the data with a linear function, quadratic function, and exponential function. They will then select the best-fitting model for the data collected and use it to predict future outcomes.Description:Students will write equations that describe the data, test a linear, quadratic, and exponential model to determine which best fits the data. Graphing calculators are permitted. Students must explain why they think that their choice is the best.Students will make a prediction on the total sales for the business in the tenth year.Student will find the annual sales for at least four years for a business or industry that interests him and make a table of the data.Make a scatter plot. Fit it to the appropriate model (linear, quadratic, or exponential).Use the model to predict future sales in five years, if you can. Explain why or why not.Student will present results in a report or a posterInclude your answers for the original question.Include all the curves that you tried and the explanations as to whether or not they fit.Describe you selected business. Explain where you found your data. Explain which model worked and which did not and why.If you used a graphing calculator or a computer to create your models, give the r-value for each and explain what they mean.Describe what you learned about fitting data to a model. (e.g. what information or values helped you to best determine the best model to use).EXTENSION: Find sales data for a business or industry related to the one you used in the previous exercise. Compare the two sets of data. Compare the growth in sales. The student will do some research to find a stock market index that you can use to compare the performance of the businesses you used in the project with the performance of stocks during the same time period.Teacher Procedures:Group students in threes so that they can simultaneously test all three possibilities and discuss which is best for the data.Have students do a paper-and-pencil scatter plot, even if they are using technology. They can then use the table to determine if the relationship is linear, quadratic, or exponential.Have students include a discussion of the r-value and how it impacts their decision.Students must be prepared to defend their choices.
Essential Skills
M6: Demonstrate understanding of, and accurately apply, place value to round off numbers.M11: Apply variables in expressions and equations to solve problems (i.e. write mathematical equations for given situation, create a mathematical model to understand the relationships between variables, or make connections between the structures of mathematically abstract concepts and the real world).M47: Solve quadratic equations by applying various tools and techniques.M21: Evaluate and employ accurate and appropriate procedures for statistical data collection, organization, analysis, and display, including making inferences and predictions, critiquing data, and drawing inferences (e.g. using normal curve and z-scores, line of best fit).M22: Interpret data to determine correlation and distinguish between correlation and cause and effect.
Scoring Guide See attached Scoring Guide
Submitted by: Lorna Tresler-Basquez, Kauai High School, [email protected]
http://www.successfulpractices.org/
Scoring GuideFitting a Model to
Data
Score Criteria
4 Students complete the table, do a scatter plot correctly, and find correct linear, quadratic, and exponential models for the data. They explain clearly why each model either fits or doesn't fit the data and include an appropriate prediction about the total sales in ten years. Students also investigate another business or industry with the same thoroughness. Reports or posters present the data clearly and thoroughly support model choices.
3 Students complete the table, do a scatter plot correctly, and find correct linear, quadratic, and exponential models for the data. They explain clearly why each model either fits or doesn't fit the data and include an appropriate prediction about the total sales in ten years. Students also investigate another business or industry, but their work is less thorough. Reports or posters present the data clearly, but model choices may not always be thoroughly supported.
2 Students complete the table and do the scatter ploy correctly, but not all models are appropriate. They include a prediction about the total sales in ten years, and investigate another business or industry. Reports or posters present the data and models, but show haste and do not support model choices.
1 Students complete the table and complete the scatter plot correctly. They do not find all the models for the data, but do include a prediction for total sales. They do not investigate another business or industry. Reports or posters are unclear and incomplete, and show little grasp of finding a model for data.
How Will I Know Students How Will I Know Students Learned It?Learned It?
Formative Assessment– Teachers moving around the room working with students.– Activities– Homework Assignments (students are allowed to correct
mistakes for credit)– Quizzes– Formal Assessments– Participation– Discussions– Rubrics
Questions?
Thank you!
