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After discussing the Shifts in Mathematical Practices with Marilyn, I feel that the elementary classes at Cub Run Elementary are on the right path of instruction. Our goal as an elementary school is to create a community of problem solvers who make real world connections and recognize the importance of mathematics by giving them the appropriate tools in their "toolbox." We spoke about the importance of teaching students HOW to think, not WHAT to think by providing students with more open-ended tasks. We agreed that it is important for students to be able to explain their mathematical thinking, and choose appropriate strategies to use when solving problems.

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Marilyn stated that she would like to create a community of learners within her classroom in which students are engaged in rigorous mathematical experiences. She stated how she wants to challenge students to think mathematically so that students have multiple opportunities to share, hear, and judge reasonableness of strategies and solutions. She wants students to learn how to persevere and attempt problems with an "I Can" attitude while making connections so that students not only see math as meaningful but FUN!

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Marilyn and I had an interesting conversation based on problem solving in the elementary classroom. Marilyn stated that problem solving has been a struggle this year because there are several students in her classroom that cannot read. She expressed her concerns for these students because, one, if they can't read, how are they supposed to analyze these problems in order to determine what is being asked of them? Marilyn stated that she knew the importance of problem solving and utilizing critical thinking skills, but she did not incorporate problem solving into her everyday routine; however, her goal was to incorporate problem solving two-three days a week

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Marilyn and I had a great discussion about the expectations of educators.  Often times teachers get caught up in teaching the content, or "to the test," especially when students reach the 3rd grade and above.  There is too much emphasis on one test that many educators lose focus on what our main goal is: to teach the students.  It is important for teachers to know their students, interests and abilities, and to teach the students on what level they are on, instead of where they should be.  In our district, We are seeing gaps in our students' education because there is too much emphasis on STAR levels and test scores.

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In order for students to realize that mathematics is important, we must make math relevant to them.  We discussed the importance of connecting mathematics to real world situations so that math becomes more meaningful to the students.  Math should not be taught in isolation!  Marilyn talked about how she tries to embed real world problems and tasks throughout her lessons so that students can make those real world connections.   Marilyn also concluded that it is not only important to make math relevant to real world, but to make connections across the curriculum as well.  Marilyn discussed how she tries to incorporate math into other subjects to interest students as well.

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Marilyn and I discussed the importance and role of manipulatives during math instruction. I thoroughly enjoyed our conversations about the use of math manipulatives and making sure that math was "concrete" for students. Manipulatives are tools that are beneficial when problem solving because manipulatives give the students a visual representation of the reasoning behind the mathematics. Students are able to see how math really works. Working with manipulatives boost students' self-confidence as well as make connections so that they gain a deep conceptual understanding of math topics.

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I feel like Marilyn is an outstanding teacher, despite being a veteran teacher that has been out of the classroom for several years.  After analyzing the Shifts in Mathematical Practices, Marilyn has reflected upon her practices to determine how she wants to change to become a better teacher for her students.  She knows her students, and wants what is best for her students.  She is determined to see that her students are successful, and is willing to try new ideas to make sure students perform at their true potential.

Oftentimes it is hard to find specific resources to utilize and enhance instruction.  Since Marilyn's goal is to incorporate more activities that encompass problem solving skills and differentiation, I have suggested that she incorporate the Daily 3 (Math by Myself, Math with Someone, and Math with the Teacher) into her instruction.  The Daily 3 will provide her the structure she needs in order to incorporate problem solving/critical thinking tasks in small groups as well as work with students on their individual levels through math conferences (individual or small group based on student needs).

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Marilyn participates in weekly primary meetings including the 2nd grade teacher, third grade teacher, Reading Recovery teacher, and the RTI/Reading Specialist in order to discuss strategies and mathematical standards/processes.  Together, this group of teachers write curriculum maps that correlate to mathematical concepts and procedures, and ensure that the "maps" flow between grade levels.

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"What is the role of a teacher in today's classroom anyway?"  Marilyn said that she still utilizes direct instruction to develop students' procedural knowledge and concepts.  Although Marilyn doesn't send homework home with her students, the students practice math skills by completing worksheets based on the skills being taught. One shift that Marilyn wanted to focus on was Shift 4, from teacher demonstrating "how to" toward teacher communicating "expectations" for learning.  We both agreed that there is a time for direct instruction, however, it should be in moderation.  I suggested that she provide her direct instruction through mini-lessons accompanied by small group/whole group activities to engage the students with the skills being taught.  Providing the students with opportunities to problem solve and discuss their mathematical thinking/reasoning with others would be beneficial to all students.   Students learn best by doing as well as from each other!  We need to step back and let the students take on more responsibility for their learning.  We need to stop thinking FOR the students and teach the students HOW to think.