New Alaska State Standards for Math Connecting Content

New Alaska State Standards for Math: Connecting Content with Classroom Practices ASDN Webinar Series Spring 2013 Session Three March 13, 2013 Measured Progress © 2011

While we are waiting to begin today, please share any print resources you have located since our last webinar, in the chat box. I would also love to hear what you thought of the PARCC Mathematics Framework- if you had a chance to look at it!

Today’s Targets §Continue to discuss the larger picturetoday’s side topic… Depth of Knowledge §Dig deeper into practices five and six: 5. Use appropriate tools strategically 6. Attend to precision §Identify key implications for classroom instruction.

Application, Application! “Ensuring that curriculum is aligned to “rigorous” grade-level content standards is, in itself, insufficient for preparing students for the challenges of the twenty-first century. Current research on the factors influencing student outcomes and contributing to academic richness and student engagement supports the concept that learning is optimized when students are involved in activities that require complex thinking and the application of knowledge. Expert teachers provide all students with challenging tasks and demanding goals, structuring learning so that students can reach high goals. Expert teachers know how to enhance both surface and deep learning of content (Hattie, 2002). Students learn skills and acquire knowledge more readily when they understand concepts more deeply, recognize their relevance, and can transfer that learning to new or more complex situations. Transfer is more likely to occur when learners have developed deep understanding of content and when initial learning focuses on the underlying principles (“big ideas”) and causeeffect relationships. ” Karen Hess (2012) 10/31/2021

Thoughts? What is the first word that comes to mind when you read this paragraph taken from the Karen Hess article?

Poll- How Important is it to Focus on Depth of Knowledge in planning? 1. Critical 2. Necessary, but not critical 3. Not so necessary 4. I would need to know more about Depth of Knowledge to answer this question. Measured Progress © 2012

The Eight Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Measured Progress © 2012

Practice Number Five Teachers who are developing students' capacity to "use appropriate tools strategically" make clear to students why the use of manipulatives, rulers, compasses, protractors, and other tools will aid their problem solving processes. In grades three and four, a teacher might have his/her students select different color tiles to show repetition in a patterning task. A teacher of students in grade five through eight might have established norms for accessing tools during the students' group "tinkering processes, " allowing students to use paper triangles to and test the angles in quadrilateral models.

Thoughts about Implementation Teachers at all grade levels might continuously ask students whether or not they are using tools to solve problems, justify their solutions, or both. Strategic use of mathematical tools build student understanding, they are not a crutch that replaces critical thinking or understanding of concepts.

Questions, Questions If you have already watched the video, and you are unable to view it during the webinar, please post a question or comment in the chat box. After we have all seen the video, we will respond to your questions or comments. Measured Progress © 2012

Using Appropriate Tools Strategically

Student Work Sample The Lattice Method/The “Salad Way”

Calculators or No Calculators? Chat box discussion! (Spoiler Alert- Julia is not going to provide any conclusive answer here…)

Poll- How about your students? How often do your students use tools strategically, to deepen understanding of concepts? 1. 3 -4 times a week 2. 1 -2 times a week 3. Once every couple of weeks 4. I am not sure what this would look like in my classroom. More is not always better…

Practice Six Teachers who are developing students’ capacity to "attend to precision" focus on clarity and accuracy of process and outcome in problem solving. An upper elementary teacher might engage his/her students in a "number talk" in which students use an in/out table and a plotted graph to "guess [the teacher’s] number. " This would promote the idea of using questioning to clarify their reasoning as to what the correct solution would be. An middle school teacher might ask students to check their answers by using another strategy to prove that they are correct.

Thoughts about Implementation Teachers of all grades might continually ask students to defend whether their answers will always be the case, or whethere are reasons to believe that they may need to refine and correct their thinking. § What happens when students are not sure? § What information can you learn about your students? Measured Progress © 2012

Questions, Questions If you have already watched the video, and you are unable to view it during the webinar, please post a question or comment in the chat box. After we have all seen the video, we will respond to your questions or comments. Measured Progress © 2012

Attending to Precision

What makes precision stand out? Why do you think the authors of the New Alaska Standards included precision as a mathematical practice? PLEASE raise your hand if you would be willing to share your answer aloud in the group. We are NOT looking for a “correct” answer here- just your thoughts. Measured Progress © 2012

What would the conversation sound like?

The Eight Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Questions, Comments, Closing Thoughts? Were there any comments or questions from the chat box that we should address before closing?

Implementation of the Practices This week’s 15 minute trade(well, maybe more like 30 minutes…) Choose one of the practices we have discussed, (1 -6) and spend one planning session for math thinking about how to concentrate on that one specific practice. What will it look like, sound like, feel like? Be prepared to share at our final webinar session. We can’t wait to hear how it went!

Be well, Do good work and keep in touch.