April 2018 - EMT Institute - Studio Day

Morning Session:
The EMT Cohort participated in a Math Studio Day, where we observed a lesson in Mrs. Bramlett's 5th Grade Classroom.  The learning goal for this experience was to recognize and enhance cognitive demand of tasks and lessons, and integrate new knowledge into our own teaching practice.

We followed the Studio Day Protocol developed by the Greater Birmingham Math Partnership.

1.  Setting up the Task - Mrs.Bramlett set the stage for the experience, providing us with the learning goals, background knowledge of students, grouping strategies, and tools students may use.
2.  Do the Math - Teachers worked the task, anticipating student strategies and misconceptions. We used a Task Analysis Guide to determine the task's cognitive demand, and we explored ways to maintain the level of cognitive demand with students throughout the task.
3.  Supporting Students' Exploration of the Task - We discussed how to help students progress through the task and understand key mathematical ideas, using assessing and advancing questions.
4.  Discussing the Task - We discussed how Mrs. Bramlett would structure her math congress (the following day).
5.  Classroom Observation - We observed in Mrs. Bramlett's classroom for one hour, which included a 15-minute number talk and 45 minutes of the investigative task.  We took notes on a graphic organizer for later discussion.

6.  Debriefing Session - EMT Teachers participated in a debriefing session to reflect on our observations and what we could take back to improve our teaching practice.

Afternoon Session
We discussed the importance of math practice and application, and explored more engaging alternatives to worksheets.  We engaged in these activities as learners!

February/March 2018 EMT Meetings

In February and March our EMT group took a deep dive into the Eight Mathematics Teaching Practices from "Principles to Actions" (National Council of Teachers of Mathematics).

We studied the first 4 practices in February and the last 4 in March.
For each practice, we read and discussed designated sections in "Principles to Actions", identified unproductive and productive beliefs, and explored what the teacher should be doing (and why) and what the students should be doing (and why).

February Meeting

1. Establish mathematics goals to focus learning
We read about writing effective learning targets and viewed a video of a TCS teacher "engaging" her students in the learning targets, and reflected on our observations.  We referenced "Leaders of Their Own Learning" by Ron Berger in our discussion.

2.  Implement tasks that promote reasoning and problem solving.
We compared three different ways to approach teaching equivalent fractions to determine which task required more critical thinking and problem solving, and why.  We participated in a Paper Folding (https://www.youcubed.org/tasks/paper-folding/) task as learners to experience a rigorous task that requires a deep level of thinking.

3.  Use and connect mathematical representations.

We learned about a Math Connections Routine we found at the NCTM Regional Conference.  After experiencing the routine as learners, grade level teams created tasks that could be used for these routines in their classrooms and facilitated these routines for our group.

 4. Facilitate meaningful mathematical discourse.
We revisited the 5 Practices for Orchestrating Meaningful Math Discussions and watched a video of Diane Briars, former NCTM President, speaking about Discussion that Advance Mathematics Learning.

March Meeting

5. Pose purposeful questions.
We discussed the purpose of both "Assessing" and "Advancing" questions.  We participated in a task with specific learning goals, anticipated student strategies, and used this to plan questions in advance.

6. Build procedural fluency from conceptual understanding.
We revisited student learning opportunities on developing fluency (from a previous session), and read more about how to build on conceptual knowledge to develop fluency.

7. Support productive struggle in learning mathematics.
We reflected individually by participating in a self-assessment on the level of productive struggle currently experienced by students in the classroom.  We read and discussed a STEM article on "Productive Struggle in Mathematics" and identified our key takeaways.

8.  Elicit and use evidence of student thinking.

We watched a video of a TCS teacher conducting a formative assessment where students pick a side of the room based on their position (a misconception debate).  Students alternate defending their position and students can move to a different side of the room if someone convinces them to change position.

Earlier this year, each teacher selected one of the 8 Teaching Practices as an area of focus.  We reflected individually on our growth and development this year regarding the selected practice.

January 2018 - EMT Institute Meeting: Fractions

We had our EMT Institute Meeting on January 2, 2018.  Our topic was Fractions! 
We started out by reflecting on 2017 and a best practice we want to focus on the first half of 2018.

Our Learning Targets for the day were:

1. I can understand the progression of fractions across grade levels.

2. I can internalize how to increase rigor with fractions.

3. I can describe the impact of number talks on understanding fractions.

We discussed how we learned fractions when we were in school, and how the focus has shifted to developing a deep conceptual understanding (versus just procedural), which requires a different approach.

Each grade level team took a deep dive into their fraction standards and presented them to the group.

We also participated in rich, investigative tasks that support the goals of developing a deep understanding of fractions.

We compared rich tasks for each grade level to approaches used to teach these concepts in the past (primarily worksheets), reiterating the importance of utilizing best practices to teach for conceptual understanding.

We discussed the crucial vertical alignment of fraction standards and related it to a tree:

• 2nd Grade - The roots are the foundation for fractions obtained from partitioning shapes and beginning to use the terminology of halves, fourths, etc.
• 3rd Grade - The trunk of the tree (the core) represents the crucial "meaning" of fractions obtained in 3rd grade; without this meaning, students cannot be proficient with standards in 4th & 5th.
• 4th Grade - The large branches represent the concepts of equivalence and decomposition of fractions, which is crucial to performing operations with fractions in 5th grade.
• 5th Grade - The many smaller branches represent the many operations students are performing with fractions in the 5th grade.
  
  
  

We examined all of the fraction number talks contained in our curriculum guides and related them to the content standards.  We realized how crucial our number talks are for students to develop proficiency with fractions.

December EMT Institute Meeting - Developing Procedural Fluency from Conceptual Understanding

Our December EMT Institute was held on December 5, 2017. Our focus was on how to develop math procedural fluency from conceptual understanding.  We discussed how we "learned" our math facts as children and how and why that has changed today.

  

We read, discussed, and analyzed NCTM's position statement on Procedural Fluency in Mathematics, as well as the vertical progression of fluency standards.  We determined the difference between "memorization" versus "from memory".

 

  

We read the article, "Three Steps to Mastering Multiplication Facts" by Gina Kling and Jennifer M. Bay-Williams, and participated in an activity where we identified tasks in each of the three phases of fluency development.  We discussed the importance of the Strategy Development phase and reviewed the strategies we are emphasizing.  We learned about addition and subtraction strategies by reading the article, "The Road to Fluency and the License to Think" by Lisa Buchhotz. We determined that the three phases for achieving multiplication fluency also apply to addition and subtraction fluency development.

The Three Phases of Fluency Development

When we reflect on how we learned our facts as children, we jumped straight from Phase 1 to Phase 3 (and attempted to memorize them.)

Phase 2 is crucial for fluency development and is a major emphasis today. Strategies are developed through tasks, number talks, and games.  Strategy development leads to fluency!

 

We reviewed barriers to fluency for upper elementary and middle school students and what we could do to reduce those roadblocks.  Some of these barriers are formed from misconceptions developed in the earlier elementary grades, such as:  1) Thinking an equation always has the answer after the equal sign, saying "the most you can have is 100% of something", using "keywords" to solve problems to simplify the process, use of the term "reducing fractions" versus "simplify", saying the product is always "bigger" than the factors in a multiplication problem, saying you "move" the decimal point, etc.

We experienced the importance of strategic number talks and purposeful games in developing fluency. We were provided with numerous games and even played some of them! We also discussed the research on the negative effects of timed fluency tests, and explored alternatives to traditional timed assessments.


Sources: 
Articles from Teaching Children Mathematics & Mathematics Teaching in the Middle School, NCTM: Three Steps to Mastering Multiplication Facts by Gina Kling and Jennifer M. Bay-Williams, The Road to Fluency and the License to Think by Lisa Buchhotz, and 12 Math Rules that Expire in the Middle Grades by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty.
Principles to Actions: Ensuring Mathematical Success for All, NCTM

November EMT Institute Meeting

Our EMT (Elementary Math Teacher) Institute meeting was held on November 2nd. The focus was how to orchestrate effective math classroom discourse, specifically with Math Congress. This is an area teachers continue to report as a challenge for them. Our group participated in the process as learners first by completing the math forum problem, "Women's Walkway".

We studied the 5 Practices for facilitating effective math discourse in the book, "5 Practices for Orchestrating Productive Mathematics Discussions" by Margaret Smith & Mary Stein.

We analyzed cases in the book and explored each of the practices by examining student work from our classrooms, and a 5th grade problem called, "John's Canvas".

The 5 practices are a framework used to manage classroom discourse, moving students toward a focused learning goal. The five practices are shown below.

We committed to becoming "Walkers & Stalkers" during the monitor phase....making sure we are walking around and listening to students' strategies.  We practiced each of these steps using student work from our schools. We also watched Mrs. Bramlett's math congress on "John's Canvas" and explored her selection and sequencing of work, as well as engagement strategies she utilized.