N E P F N evada E ducator P erformance F ramework Southern Nevada Regional Professional Development Program Standard 3 Part 2 Secondary Mathematics

Standard 3 Module for Mathematics Part 1 – What and Why Goal 1: What is Standard 3? Goal 2: What are the indicators for Standard 3? Part 2 – Implications for Mathematics Goal 3: What student learning tasks would provide evidence of the standard? Goal 4: What specific tasks can be designed and/or adjusted to implement them?

NEPF Standard 3 Students Engage in Meaning Making through Discourse and Other Strategies Classroom environment enables collaboration, participation and a positive, affective experience for all students. 4 Opportunities for ALL students to create and interpret multiple representations that engage student thinking. 2 Opportunities forextended,productiveDISCOURSEbetween theteacher andstudent(s) andamong students. 1 Use existing knowledge andprior experience to make connectionsand recognizerelationships tofurther acquisitionof skills. 3

THIS STANDARD IS SAYING THAT… Students should be active in making meaning during their own learning. Teachers can support students’ meaning making by: 1) engaging them in productive discourse (Indicator 1); 2) involving them in creating and interpreting multiple representations (Indicator 2); 3) connecting what they are learning to what they already know (Indicator 3); and 4) structuring a positive classroom environment to enable collaboration and participation (Indicator 4).

Showing evidence… MANDATORY EVIDENCE SOURCES OF INSTRUCTIONAL PRACTICE OPTIONAL EVIDENCE SOURCES OF INSTRUCTIONAL PRACTICE DIRECT EVALUATOR OBSERVATION ONE CONFIRMATORY ITEM FROM OPTIONAL EVIDENCE SOURCE ONE ARTIFACT OF THE REPRESENTATION AND/OR ITS CREATION, INTERPRETATION, OR USE OF THE REPRESENTATION TEACHER PRE/POST CONFERENCE TEACHER NOTES AUDIO/VISUAL/PRINT ARTIFACT LESSON PLAN STUDENT WORK STUDENT FEEDBACK

What do Teachers Need to Demonstrate as Evidence for Standard 3? LOOK FORS:LISTEN FORS: In teacher planning: What artifacts are available that guide the planning of lessons? Do teacher notes, student work, and collaborative activities show planning and forethought? In class (teacher): How are students engaged in discourse? How effective are aspects of classroom environment, routines, expectations, and communication? In student work: What is the quality and depth of the discussions? Are verbal and/or nonverbal representations seen? In class (student): How are students engaged in discourse? Is thinking externalized? Are arguments, explanations, and critiquing evident?

Teachers can support students’ meaning making by providing opportunities for extended, productive discourse. How do teachers promote this discourse?

Promoting discourse?!

 Change from “How can I teach students to get the answer to this problem?” to “How can I use this problem to teach the mathematics of this unit?”  Ask How did you do it? How do you know your solution is correct? What would happen if (give a variation).... ? We encourage discourse between teacher and student when we…

We can promoteby engaging students in interactive dialogue meaning-making explaining, critiquing using logic and evidence to support or refute a claim Simple Paired Activities Homework Checking Pairs Think/Pair/Share Question and Answer Pairs Note-Checking Pairs Group Activities Cooperative Learning Cubing I Have – Who Has Matching Problem Solving How do we provide opportunities for discourse among students?…

Activity:_________________________ Activity Purpose/Benefit ___Hear ___See ___Say ___Do ___Write ___Problem-solve (Application) ___Organize information ___Solve ___Procedures ___Explain (to others/peers, class) Level of Engagement Check List

Resources for Standard 3, Indicator 1 Check our resource list for templates, descriptions, etc. for group activities. Look for Active Learning for Mathematics at > NEPF >math resourceswww.rpdp.net

Teachers can support students’ meaning making by involving them in creating and interpreting multiple representations. How do we create tasks that challenge students to create and use these representations?

What are “representations”?

models diagrams writing digital and print media images/visuals graphs and tables videos simulations patterns concept maps drawings Challenge students to create and use representations that include:

Mathematical Practice # 4: Model with Mathematics Modeling is a common thread found at every grade level in the Nevada Academic Content Standards for Mathematics

What does Math Modeling Mean? This video addresses the mathematical practice Create a Mathematical Model from the Common Core. Students are often confused about what a math model actually encompasses. Start at 0:20

N A G Use NAG to create multiple representations…. A LGEBRAICALLY y = x G RAPHICALLY N UMERICALLY xy

MODELING: Strategies to Solve Ratio Problems Common Core: 6.RP.3a, by Kathryn Newmark “Choose a strategy to solve ratio problems” In this lesson you will learn to solve ratio problems by choosing the strategy you like the best. Start at 1:36

MODELING: Simplify Square Roots Using Physical Models Common Core: N-RN.2, by Lauren Burton “Simplify square roots using physical models” In this lesson you will learn how to simplify square roots by examining physical models.

Teachers can support students’ meaning making by connecting what they are learning to what they already know. How do we create tasks that help students to make these connections?

Connect to Prior Knowledge How? Using graphic organizers; KWL charts, Venn diagrams, etc. Sound familiar? The “prior knowledge” connection is NEPF Standard 1! Refer to the resource materials presented in the module for Standard 1.

Use a High Yield Strategy Identifying similarities and differences is the #1 high yield strategy for increasing student achievement.* STUDENTS SHOULD :  Compare, classify, and create metaphors, analogies and non-linguistic or graphic representations  Use Thinking Maps, T-charts, Venn diagrams, classifying, analogies, cause and effect links, compare and contrast organizers *Classroom Instruction that Works: Research-based Strategies for Increasing Student Achievement, by Robert Marzano (2001)

Venn Diagram: Compare & Contrast Topic: Summary: UNIQUE SAME UNIQUE

More thoughts on making connections: Help students use their prior knowledge to draw analogies that support their understanding of the concepts.

Using Analogies in Math Classes To create analogies, students must understand relationships, such as comparing, contrasting, and sequencing. Start with a simple example from other disciplines. hot : soup as cold : _______ (ice cream) Then try: straightedge : line as compass : ______ (circle) ray : line as arc : ______ (circle) parallel : intersecting as acute : ______ (obtuse) 4 : 12 as 1 : ___ (3) ½ : 50% as ¼ : ___ (25%)

Additional Thought on Indicator 3 Recognize that students bring a variety of personal experiences to the classroom. For strategies to address this diversity, refer to the resource materials in the module for Standard 2!

Teachers can support students’ meaning making by structuring a positive classroom environment to enable collaboration and participation How do we create such an environment?

Creating a positive classroom environment?

Building Classroom Community Teachers need to consider factors in classroom environment: Classroom CultureClassroom Management NormsStudent behavior RoutinesResource provision ExpectationsOrganization of physical space Communication patterns

Encouraging environment?

Notes from brain research… Once sensory information enters the brain, it’s routed to one of two areas: (1) the prefrontal cortex, what might be called the thinking brain, which can consciously process and reflect on information; OR (2) the lower, automatic brain, what might be called the reactive brain, which reacts on information instinctively rather than through thinking.

When a student is anxious, stressed, sad, frustrated, confused or bored, brain filters conduct the sensory information into their reactive brain. If information gets routed to this reactive brain, it is unlikely the brain will process the information or remember it. That is, unless a positive mood is restored, the student won’t be learning much on this particular school day. THEREFORE, if a student is stressed, they CAN’T use their thinking brains…

Classroom-related stressors must be eliminated to enable collaboration, participation, and a positive experience for all students.

While watching the following video clip, look for: Students working collaboratively Discourse Viable suggestions/arguments Sharing ideas/thoughts k-pair-share-lesson-idea k-pair-share-lesson-idea Standard 3 in action

Think-pair-share video

Did the activity (in the video) address... Standard 3: Students Engage in Meaning-Making through Discourse and Other Strategies Productive discourse? Multiple representations? Prior knowledge and experience? Conducive environment for collaboration?

In summary... Teachers support students in making meaning of their own learning Engage in productive discourse Involve students in creating & interpreting multiple representations Structure a positive classroom environment to enable collaboration & participation Connect what students are learning to what they already know

What evidence of Standard 3 can you visualize in your classroom? Name 3 artifacts you are already using. What new strategies or ideas (using Standard 3) do you think you could use in your classroom? Give 2 such examples. Commit to using a new strategy. What 1 strategy will you employ? “3 – 2 – 1”

NEPF Standard 3: Students Engage in Meaning Making through Discourse and Other Strategies

For additional NEPF resources rpdp.net Select NEPF