1. Teaching Mathematics for Learning A Standards Aligned System
Secondary Mathematics Teacher Leadership Academy
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

2. Math & Science Collaborative
Norms for Learning
What can you do to make this a good learning experience for yourself?
What can you do to make this a good learning experience for others?
Have participants share out. Add any of their ideas to the next slide as well as discuss what’s already there.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

3. Professional Practice Norms
Listening to and using others’ ideas
Keeping records of professional work
Adopting a tentative stance toward practice - wondering versus certainty
Backing up claims with evidence and providing reasoning
Talking with respect yet engaging in critical analysis of teachers and students portrayed
Seago & Mumme, 2003
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

4. PA Standards Aligned System
GOALS:
Define Standards Aligned Systems, identify its purpose, and understand all segments of the system
Investigate the relationship between the PA standards and assessment anchors to the Big Ideas, Concepts, and Competencies
Explore the Big Ideas in math to search for links within curriculum and instruction
As we look more deeply at the Standards Aligned System, these are our goals.
We want everyone to know what the Standards Aligned System is and how it can help you in your classroom.
We want everyone to understand the relationship among these tools provided for us by the state.
We will be linking the big ideas and competencies in math to curriculum and instruction.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

5. What Is SAS? The Pennsylvania Standards Aligned
Systems (SAS) is a collaborative product
of research and good practice that
identifies six distinct elements which, if
utilized together, will provide schools and
districts a common framework for continuous
school and district enhancement and
improvement.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1 5

6. Standards Aligned Systems
This graphic helps to visualize a SAS which can be seen on Ed Hub and which must all work together as a system.
All pieces are necessary for the whole puzzle to be completed. All of these work together to help a district improve student achievement.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1 6

7. Math & Science Collaborative
Clear Standards
Establish what all
students should know
and be able to
accomplish.
Standards are the minimum of what we must teach our students. We can and should maximize and go beyond our standards. Anchors are just testable items.
Standards must drive what we prepare as curriculum and learning for our students.
Pennsylvania standards describe what students should know and be able to do and reflect the increasing complexity and sophistication that students are expected to achieve as they progress through school. The Assessment Anchors clarify the standards assessed on the PSSA and can be used by educators to help prepare their students for the PSSA. We use the metaphor of an “anchor” because we want to signal that the Assessment Anchors anchor both the state assessment system and the curriculum/instructional practices in schools.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

8. Math & Science Collaborative
Fair Assessments
Aligned to PA Standards
Summative
Formative
Diagnostic
Benchmark
Summative Assessment: seeks to make an overall judgment of progress made at the end of a defined period of instruction. They occur at the end of a school level, grade, or coursed, or are administered at certain grades for purposes of state or local accountability. These are considered high-stakes assessments.
Formative Assessment: The primary purpose of the formative assessment process is to provide evidence that is used by teachers and students to inform instruction and learning during the teaching/learning process. Effective formative assessment involves collecting evidence about how student learning is progressing during the course of instruction so that necessary instructional adjustments can be made to close the gap between students’ current understanding and the desired goals. Diagnostic Assessments: the purpose of diagnostic assessment is to ascertain, prior to instruction, each student’s strengths, weaknesses, knowledge, and skills. Establishing these permits the instructor to remediate students and adjust the curriculum to meet each pupil’s unique needs. Examples of diagnostic assessments are: DRA’s, Running Records, GMADE Benchmark Assessments: are designed to provide feedback to both the teacher and the student about how the student is progressing towards demonstrating proficiency on grade level standards. They: measure the degree to which students have mastered a given concept, measure concepts, skills, and/or applications, are reported by referencing the standards, not other students' performance, serve as a test to which teachers want to teach, measure performance regularly, not only at a single moment in time. Examples of benchmark assessments are: Pennsylvania’s benchmark assessment - 4Sight, Scantron, ,DIBELS
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

9. Math & Science Collaborative
Curriculum Framework
A framework specifying Big Ideas,
Concepts, and Competencies
in each subject area/at
each grade level.
A curriculum framework specifies what topics are to be taught at which grade levels for each subject in the curriculum. At any given grade level, the topics that are taught are those-and only those-that are needed to provide the foundation for what comes next. In Pennsylvania, we are developing curricular frameworks that are built by identifying standards, anchors, big ideas, concepts, competencies, essential questions academic vocabulary, and exemplars.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

10. Math & Science Collaborative
Instruction
Aligned with standards in order
to identify strategies that
are best suited to help
students achieve the
expected performance.
Aligned instruction comprises the following activities:
Teaching topics that are aligned with the standards.
Making sure that you get the right level of challenge. Instruction that is too challenging leads to frustration and discouragement on the part of students. Instruction that is not challenging enough results in little or no learning.
Focusing teaching based on the learning needs of each student. These needs are those identified through evaluation of student achievement against the standards.
Implementing instructional strategies that 'scaffold' by building on each other to help students achieve the standards.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

11. Math & Science Collaborative
Materials & Resources
Chosen as a guide for selecting
material from textbooks,
reading materials, software,
and any other instructional
resources that are needed
to fit the framework
and match the standards.
The Voluntary Model Curriculum will be strictly aligned to the PA standards, concepts, and competencies a well as the assessment anchors. It will include learning progressions, units, and lesson plans. The learning progressions will span grades K-12, including what students should know as a result of successfully moving through grades K-8 and by taking specific courses in grades 9-12.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

12. Math & Science Collaborative
Interventions
A safety net/intervention
system ensures
all students meet standards
The purpose of safety nets is to ensure students are provided with supports they need to meet and or exceed grade level standards as quickly as possible. The foremost safety net is to ensure that students attend school and are ready to learn. Decisions regarding student entry to and exit from safety net programs should always be made on the basis of data. What we know from data indicates that early intervention is essential; safety nets are those built into the structure of regular classroom. A comprehensive system of safety nets involves a graduated set of interventions.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

13. Why do we need a Standards -Aligned System in Pennsylvania?
To support districts with Curriculum, Assessment, and Instruction
To provide Professional Development
To promote an ongoing learning community
To help all students meet and when possible, exceed the PA Academic Standards
Enable our students to be competitive in a global market
Online community of educators collaborating to make the best instructional decisions for their students
Ongoing learning community to aid in the potential of the teacher which will then support the students progress
A repository of ideas and resources all aligned to the PA academic standards and the Big Ideas in each content areas
We want them to go beyond the standards
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1 13

14. Number of Mathematics Topics Intended
In addition to the previous slide, other findings came out the TIMSS research.
This data was collected from teacher surveys at schools where students were taking the TIMMS test. Therefore, this data was reported by teachers themselves as to how many topics are in the grade level curriculum they teach each year. As you can see, the number of topics reported by US teachers was significantly greater than the number of topics found at each grade level in top achieving countries. And Southwest PA, (represented by the blue triangles on the right) is almost “off the chart” in terms of the number of topics at each grade level.
How can we teach for deep conceptual understanding when we are trying to teach more than 25 topics in 9 months?
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

15. Number of Mathematics Topics Intended
One set of a coherent set of mathematics standards for first through 8th grades appears in the figure on the left, which represents the grade level expectations in a majority of top-achieving countries in TIMMS. The structure of the data display makes its implied coherence self-evident.
By contrast, the figure on the right shows the content standards for three US states. The arbitrariness of these curriculums contrasts sharply with the coherence of the curriculums depicted on the left. The lack of coherence makes in-depth learning of demanding mathematics more difficult for all students, especially at-risk students.
The TIMSS study characterized U.S. curriculum as “as a mile wide and an inch deep,” and attributed that to a splintered vision.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

16. Math & Science Collaborative
Definitions
Big Ideas – A declarative statement of enduring understandings, for all students at each grade level/course.
Concepts – What students should know.
Competencies – What students should be able to do.
Big Ideas highlight the key learnings at each grade level or course for all students – this helps set priorities
Big Ideas are dedicated to understanding, permanent learning, and success at higher mathematics – they span several grades.
Concepts help set what students should know and Competencies outline what students should be able to do
Big ideas – can span various grade levels
Concepts – are nouns
Competencies – what’s the ultimate competency you want to see.
What are the 5-6 things you want every 6th grade to know & then you want them to demonstrate it. As you pick curriculum and inst strategies, you utilize your Big ideas & competencies
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1 16

17. Competencies Answer the Question…
What is the essential mathematical learning at this grade level or in this course?
Read .. So…for example knowing mean, median, and mode is not a big idea but rather Displaying, Analyzing, and Making Predictions Using Univariate and Bivariate Data Gathered from Real World Situations is a big idea.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1 17

18. Math & Science Collaborative
So….
How can we identify and organize a few essential learnings at each grade level?
What might the curriculum look like as it’s organized around essential learnings in mathematics?
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

19. Navigating the Website
Math & Science Collaborative

20. Building a Knowledge Network
In your group identify the one card representing an essential learning of mathematics, which would incorporate the concepts of all other cards.
Sort the other cards into two piles by common content.
Discuss that there are building blocks of knowledge that make up the competencies. Have participants engage in the following two slides to create a knowledge network that is revealed on slide 30.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

21. Building a Knowledge Network
From each of the two stacks, identify the one card representing a Key Component, which would incorporate the content of all the remaining cards in that stack.
Place these two cards underneath the essential learning.
Organize the leftover cards under the correct Key Component.
Math & Science Collaborative

22. Collect, Organize and Display Data
Display, Analyze, and Make Predictions Using Univariate and Bivariate Data Gathered from Real World Situations.
Algebra 1
Problem Solving, Reasoning, Communications, Connections, and Representations should be integrated throughout the web.
Continue to Use Statistical Methods to Analyze Data, and Evaluate Inferences and Predictions Based on Data
Collect, Organize and Display Data
Use, create, and interpret scatterplots.
Evaluate different graphical representations of the same data to determine which is the most appropriate for an identified purpose.
Differentiate between discrete and continuous data and utilize appropriate ways of representing each.
Understand the influence of scale in creating and interpreting data displays.
Compare two sets of data using measures of center, (mean, median, mode) and measures of spread (range, quartiles, interquartile range).
Make conjectures about possible relationship in a scatterplot and approximate line of best fit.
Investigate the different effects that changes in data have on the mean and median.
Understand that the measure of center alone does not thoroughly describe a data set.
This is a knowledge network which we’ve developed which links the competencies at each grade level to the building blocks for that competency.
Select mean or median as the appropriate measure of center for a given purpose
Construct convincing arguments based on analysis of data and interpretation of graphs.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

23. Standards Aligned System: Mathematics
Take a few minutes to look at the big ideas, concepts, competencies, and knowledge networks for one grade level.
What did you notice?
Possible responses:
There are not a lot of competencies.
The big ideas are huge.
Some grade levels have the same big ideas.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

24. Standards Aligned System: Mathematics
The Pennsylvania Standards Aligned
Systems (SAS) is a collaborative product
of research and good practice that
identifies six distinct elements which, if
utilized together, will provide schools and
districts a common framework for continuous
school and district enhancement and
improvement.
We will be coming back to this framework in each of our sessions.
Math & Science Collaborative
SAS Secondary Mathematics Teacher Leadership Academy, Year 1