Lesson-Design Elements That Reflect the College-and Career-Ready Standards for Mathematics and the Standards for Mathematical Practice. / 90 minutes
Materials: Session Handouts:
Chart paper
Participants will:
- Review standards for mathematical practice and reflect on implications for instruction.
- Reflect on criteria used to evaluate mathematics lessons and tasks.
- Determine important criteria to assess mathematics lessons that exemplify College and Career Ready
Lesson Flow / Research/Helpful Hints
/ Before: Engage
Slides 1 & 2
Welcome participants to the second CCRS meeting.
Have participants think about the last meeting, specifically the session on K-5 Standards for Mathematical Practice (SMPs). Tell them to turn and talk to their shoulder partner about how they used the information presented at that CCRS meeting.
Allow participants time to share ideas with the entire group.
Share session outcomes with the participants. / 5 minutes
Please allow participants to make connections from the first CCRS quarterly meeting during this time. Explain that this session is based on their comments from the last session.
/ Show slides 3, 4, 5 & 6.
Have participants briefly discuss with a shoulder partner what each slide means.. Allow a volunteer to share with the entire group. Explain to participants that the CCRS meetings support our Alabama Quality Teaching Standards.
Rationale. Researchers identify a strong relationship between teachers’ content knowledge and the achievement of their students.
Rationale. Instruction and assessment are the vehicles by which teachers design and deliverrigorous and relevant learning experiences for all learners. Research provides compelling evidence relating student achievement to teachers’ use of appropriate instructional strategies selected froma rich repertoire based onresearch and best practice.
Rationale. Current research relates teacher collaboration, shared responsibility for studentlearning, and job-embedded learning in professional communities to higher levels of student
achievement. This research challenges the independence and isolation that has historicallycharacterized the teaching profession and calls for de-privatization of practice.Beyondcollaboration, teachers exhibit professionalism by demonstrating a personal commitment to continuous learning and
improvement;
/ Show slide #7
Allow participants time to read the slide. Remind them that this quote comes from the CCSS.
Show slide #8
Say, The authors of the Common Core were very intentional in the development of the standards for mathematical practice. We need to review the standards for mathematical practice for our work today.
Show slide #9
Divide the participants into eight groups. Assign each group a practice. (Use the mathematical practice cards for this activity)
Provide each group with a sheet of chart paper. Have the groups create a graphic organizer (Frayer Model) to illustrate their practice standard.
Allow each group 1 minute to share highlights of the groups’ discussion.
Show slide #10
End the discussion by having participants reflect on the statements on the slide. / 25 minutes
The Frayer Model is a word categorization activity that supports the development of the understanding of important concepts. There are many variations of the Frayer Model, but most include the Essential Characteristics of the concept as well as Examples and Non-Examples. The use of examples and non-examples is a concept attainment strategy.
It is important that participants understand that SMPs connect students’ learning to the content.
/ During: Explore/ Explain
Show slide # 11
Have participants view video clip: 4th Grade: Can This Be True?
Using the “What does instruction for Mathematical Practice look like” handout, have participants discuss the video clip in small groups. Allow participants to share thoughts about the questions.
Have participants discuss and identify important criteria that should be used to evaluate a mathematics lesson that addresses college and career standards.
Show slide # 12
Explain to participants that exemplar consist of several major components.
•The lesson targets grade level mathematics standards and identifies specific standards.
•Selected standard(s) for mathematical practice relate directly to the learning target.
•Includes multiple forms of assessment for learning.
•The lesson presents a balance of mathematical procedures and deeper conceptual understanding of mathematical ideas and concepts.
Have participants briefly discuss how the lesson addresses the components listed on the slide.
Show slide #13.
Explain to participants that conceptual understanding must precede procedural fluency.
Use the facilitator notes to help participants understand the importance of developing conceptual understanding.
Therefore, teachers must seek to develop students “understanding” of the big ideas by promoting conceptual understanding of mathematical ideas. Ask, “How did the lesson in the video promote conceptual understanding and procedural fluency?”
Now have participants work in groups to brainstorm a list of criteria used to evaluate exemplar lesson.Remind them that exemplar lessons promote conceptual understanding and procedural fluency, and address the needs of all learners. Encourage participants to be prepared to justify their criteria. Allow groups time to discuss and make group lists of criteria. / 30 minutes
4th Grade: Can This Be True?
- What did you notice about the lesson?
- Were you able to identify the lesson objective?
- Which SMPs did you notice? What would be the evidence?
- What forms of assessment did you notice?
/ After: Extend
Show slide # 14with the following questions:
- What is it you want students to know?
- How will you know if they’ve learned it?
- What will you do if they don’t learn it?
- What will you do if they already know it?
Using the questions on the slide, have participants discuss the pre lesson planning /post lesson planning. .
Next, have participants reflect on group lists of criteria by discussing if their criteria will address these questions.
Finally, allow groups to share highlights from the discussion. / 25 minutes
4th Grade: Can This Be True?
The goal of this activity is to have participants determine how the teacher addressed the questions during the pre and post planning.
Participants discussions should focus on :
- Content
- Assessment (RtI)
- SMPs
- The balance between procedural fluency and conceptual fluency
Be sure to encourage administrators to discuss their role in helping teachers implement the standards as they develop math lessons.
Lesson Reflection
/ Show slide # 15
Have teachers reflect on questions 3 & 4 on their note taking tool.
- What are the most important components of an exemplary K- 5 math lesson? How will this information help teachers?
- What criteria would you use to evaluate K-5 math lessons that promote college and career readiness?What information from this session is important for teachers to know? How should they be informed?
B. Title of Activity/Lesson / Time Allotment
Lesson-Design Elements That Reflect the College-and Career-Ready Standards for Mathematics and the Standards for Mathematical Practice. / 90 minutes
- Evaluate lesson plans according to specified criteria (Standards, skills, assessment)
- Understand how to standards for mathematical practice intersect with content standards to develop student understanding.
Research/Helpful Hints
/ Show Slide: #16
Ask participants “What is a Lesson Study*?”Allow a couple of participants to respond. Now share the definition on the slide and use facilitator notes to explain the background and purpose of the lesson study.
Say, “We spent the first part of our work today determining effective criteria used to evaluate / assess mathematics lessons in terms of SMPs, content Standards and assessment practices. The next part of our work will focus on simulating a grade level lesson study. Now we need to divide into two primary learning groups: K-2 and 3-5.
Allow participants time to decide how to divide into groups. Your groups will depend on the number of participants and the grade band they decide to explore. For example, if you have 20 participants and 15 decide to work with the 3-5 grade band you should have 3 groups of 5 for the 3-5 grade band and 1 group of 5 working with the K-2 grade band (groups can be different sizes). Explain to participants that this session will concentrate on developing an understanding of grade level expectations for evaluating mathematics lessons and tasks. / 5 minutes
*Lesson study is a professional development process that Japanese teachers engage in to systematically examine their practice, with the goal of becoming more effective. This examination centers on teachers working collaboratively on a small number of "study lessons". Working on these study lessons involves planning, teaching, observing, and critiquing the lessons. To provide focus and direction to this work, the teachers select an overarching goal and related research question that they want to explore. This research question then serves to guide their work on all the study lessons.
/ Show slide #17.
Ask participants, “How should teachers determine what to teach?” Tell participants to think about how they determine what mathematics content is taught in their classrooms. Show video clip of Dr. Bice discussing one of his five absolutes of education. Explain to participants that Dr. Bice expects us to teach the standards.
Share slide #18
Say. “Lesson studies begin by deciding what it is that students need to know”, Basically, beginning with the end in mind.”
Today we have pre-determined what we want students to know. However, we will explore the process of understanding and identifying the big idea.
Provide participants with copies of the K-2 and 3-5 lessons. Explain to participants that these lessons were selected from units of study on NCTM’s Illuminations website.
Show slide # 19.
Tell participants to work in groups to read and talk through the lesson. Make sure that participants have all of the materials to demonstrate the lesson with their groups. Encourage participants to roll play the lesson using the materials. Explain to participants that they need to use this time to become very familiar with the lesson. / 15 minutes
Dr. Tommy Bice on the 5 Absolutes of Education in Alabama:
Suggestion: Have participants read the lesson individually before group discussions begin.
Note: During this portion of the training participants should
- Read the lesson
- Simulate the lesson
- Discuss the lesson
/ Show slide # 20.
Say, “Although the lesson has been identified, your groups will need to work together to identify which standards are addressed in this lesson.”
Have participants explore the standards for each grade in their grade band.
Show slide #21.
Explain to participants that slide 12 illustrates how content standards are organized.
Show slide #22.
This slide is hyperlinked to the Alabama Insight presentation from the first quarterly meeting.
If participants are not familiar with the tool, briefly demonstrate the process of logging in and finding standards.
Allow participants time to identify and discuss standards. / 20 minutes
See the Alabama Insight facilitator notes from the first quarterly meeting.
Note: The most effective way to facilitate the standards insight portion of this session is to demonstrate the log in process with the entire group and then work with individual groups as needed.
Provide participants with the username and password
guest
guest
/ Show slide 23.
Say, “Now that we’ve identified the standards, we can use the standards’ insight tool to help us with content.
Have participants use the Alabama Insight tool to identify the content by identifying the knowledge and understanding associated with each standard.
Allow participants time to discuss their findings in their groups. / 5 minutes
How do the activities in the lesson support the understanding required by the standard?
Can you describe how the activities connect to the standards?
/ Show slide #24.
Say, “Let’s look at standards in terms of what students will need to be able to do. How can we use the insight tool to help us identify this information?
Participants should recognize that the tool unpacks each standard in terms of skills and evidence of attainment. Teachers should use the tool to help them know what students will be able to do in order to achieve/ meet the standard. / 5 minutes
/ Show slide # 25.
As we plan exemplary lessons, we must be mindful of all populations of students we serve. High end learners and students not performing at grade level are often overlooked.
Our gifted and talented students require challenging curriculum in order to thrive and grow academically. One specific thing we can do for students not performing at grade level is to utilize resources such as the Alabama Curriculum Guides.
Show slides 26 & 27.
We would like to make sure everyone is familiar with the Alabama Curriculum Guides.
The Alabama Curriculum Guides can be useful for all students, not just students with disabilities!
They are designed for students who are not performing at grade level and they include objectives that are prerequisite to the standard and/or break the standard down into smaller instructional units.
Show slide 28.
The Alabama Curriculum Guides prepare students for study of the grade-level standards through the teaching of prerequisite and enabling skills necessary for learning each content standard.
This allows students to work toward grade-level and course content standards while working at individual ability levels.
By identifying the prerequisites and enabling skills for each standard, teachers may plan instruction to address the achievement gap experienced by some students while still working with all students toward achievement of the same standards.
Show slide 29.
The Alabama Curriculum Guides for each core content area can be accessed from the Special Education Services page on ALEX. / During this time be sure to encourage participants to discuss how the lesson addresses the needs of all learners. Examples include:
- Manipulatives
- Whole group and small group
- Technology
/ Show slide #30.
Say,“Now we have come to one of the most important components of an exemplar lesson- assessment. In your group discuss evidence of various types of assessments within the lesson. How do these assessments target students’ achievement of a skill or concept?” / 5 minutes
Allow participants time to explore the assessment opportunities within the lesson. Ask, “Are the assessment opportunities adequate? How does the assessment relate to the learning target?
/ Show slide #31.
Say, “We have just gone through a quick process of studying a lesson to determine its effectiveness in terms of the big idea, standards, content, skills and assessment.
Show slide 31
That was the “what”;Let’s move to the “how” of the lesson.
How will students learn this skill/concept? You have a copy of a CCSS mathematical practice lesson planning tool in your handouts. Please use the tool to review your lesson.
Determine what practices are embedded in the lesson or identify changes you would make to make the practices more explicit in the lesson. You may also modify the mathematical tasks to accommodate mathematical practices.
Show slide # 33.
Have participants work in groups to review the lesson by the using the CCSS mathematical practice planning tool. Provide each group with chart paper and markers. Tell them to identify the learning target and the standards that support the target. They should also include the task (s) that will be used to address the target and the targeted Standard for Mathematical Practices. Tell groups to be prepared to explain how the practice relates to the learning target.
Allow each group time to share their posters and address comments / questions.
Show slide #34.
Have participants take out their individual lesson plans. Tell them to evaluate their lessons according to the same criteria we used to evaluate the exemplary lessons. Encourage teachers to discuss their findings within their small groups.
Show slide 35.
Explain to participants that they will go back and teach their lessons. Encourage them to take notes or video tape the lesson so that they will be able to discuss their lesson at the next quarterly meeting. / 25 minutes
Lesson studies can take hours, days or even weeks. This was a very abbreviated version of a lesson study.
As you facilitate groups encourage participants to think about how this process could be modeled in grade level meetings. Be sure to have administrators to discuss their role in helping teachers engage in lesson studies as they develop college-and career-ready lessons.
Lesson Reflection
/ Show slide # 36