Making Connections in Mathematics Teri Calabrese-Gray

Focus, Coherence, Rigor We must continue to focus on the three major shifts in mathematics: Focus, Coherence, and Rigor Focus – fewer topics per grade level and greater depth Coherence – seeing connections Rigor – balance conceptual understanding, procedural fluency and meaningful applications of mathematics A quality mathematics program MUST have all three of the above!

Revision of the NYS Mathematics Standards

Revision of the NYS Mathematics Standards Update: The NYS Content Advisory Panel (CAP) met in December and reviewed the public comment. Revisions were made based on the feedback. As a member of the Standards Review Leadership Team, I led the geometry group. This group probably had the most changes from the work that was done in July. The groups are still working on the Probability and Statistics strand, grades 6 – high school.

Revision of the NYS Mathematics Standards Update: In January, members of the NYS Mathematics PD Framework group, assisted the Department, in the review of the CAP work and now it is out for review with various stakeholder groups, as well as back to the leadership team to work on introductions to the grade bands and courses. The Department is still aiming for a spring adoption.

Revision of the NYS Mathematics Standards Update: I have spent the last two years struggling with the work that is going on in my region, rest of state, as well as the nation. I have been examining the various resources out there and still believe the NYS math modules are quality. The unfortunate thing is that they are not packaged in a box with a pretty little bow.

Open Up Resources I sat in on a webinar last week with Bill McCallum, one of the original authors of the Common Core State Standards. I encourage anyone who has the chance to listen to Bill because he “gets it”. He started Illustrative Math and is currently leading Open Up Resources http://openupresources.org/instructional- materials/mathematics/. Open Up Resources is a nonprofit developing the highest quality full-course curricula, provided for free to promote instructional equity.

Open up resources They developed a Grades 6-8 Mathematics Curriculum and I would recommend people to review it. They piloted this year and are in the process of making final revisions. It will be available for purchase this summer.

Standards and Curriculum Middle school math had been a “black hole” for a long time and the curriculum pretty much looked the same each year. Things have definitely changed for the better and we are challenging students, as well as teachers. Standards define the “what” we need to teach and Curriculum outlines “how” we teach/sequence the content. In the past, many used standards as curriculum by simply putting the standards in a particular order as to when they should be taught. Many were just a bunch of isolated facts.

Curricular Coherence When developing a mathematics curriculum, it is important to connect the mathematics. For example, grade 3 students begin multiplication and introduce area. Why do we teach multiplication and then teach area later, why don’t we teach them together?

Curricular Coherence Let’s give purpose to multiplication. We must weave them together, but teachers need to know how to make those connections so they can help their students do the same.

bolded Curricular Coherence William Schmidt and Richard Houang (2002) define curriculum as coherent if it is “articulated over time as a sequence of topics and performances that are logical and reflect, where appropriate, the sequential or hierarchical nature of the [discipline] … standards must evolve from particulars to deeper structures inherent in the discipline. These deeper structures then serve as a means for connecting the particulars…” Note the three pieces of the definition bolded above.

Curricular coherence Trying to tie things together is very powerful and helps establish fundamental structures all students must know. Open Up Resources attempted to make connections in the lesson plan between topics, types of lessons and types of activities.

A beginning, middle and end The standards are a list of skills and understandings all students should have by the end of the year. Curriculum is a sequence of learning experiences. He made the analogy of mathematics as being stories that have a beginning, middle and end. We usually want to go straight to the end. It is critical to develop a sequence of activities to get you there.

Activity: Prisms AND cylinders I brought an activity today and want you to work with two other partners and then another team to make as many connections as possible. Think about the mathematics, other content areas, as well as the NYS Teaching Standards as you work through the activity. We will debrief once we complete the activity.

Activity: Prisms AND cylinders At your tables you have the following items to complete the task: Popcorn Prisms Anyone? Handout Popcorn Cylinders Anyone? Handout White Pieces of Paper (Each team needs two sheets) Pieces of Paper (Each team needs two sheets) Rulers Cereal (Substitute for Popcorn) Paper Plates (Each team needs 1) Styrofoam Cup (Each team needs 1 cup) Calculators (Please feel free to use your smartphone – turn sideways for scientific)

Activity: Prisms AND cylinders At least one team at your table is going to work on the Prism handout and another team at your table will work on the Cylinder handout. However, before we begin I want to pose a few questions. You are going to make a prism/cylinder with one sheet of paper by folding lengthwise and another prism/cylinder widthwise. Make a prediction: Would one prism/cylinder hold the same amount of cereal as the other or would one hold more than the other? I am going to give you 30 seconds to think about the question I just posed and then discuss with your team members. Justify your answer.

Team Time: complete questions 1-5 Challenge Questions: 6-7 Prism Handout and 6-8 Cylinder Handout

Activity: Prisms AND cylinders 2. Now let’s compare our work. Prism A Volume: Prism B Volume: Cylinder A Volume: Cylinder B Volume: 3. Which has the largest volume overall? Why?

Identifying connections Now let’s look at the Connections. Brainstorm at your table as many Connections as possible. (Utilize all the documents available to you and what you know about other standards.) Take Aways??

Identifying resources to go along with the standards What resources should SED provide in addition to the standards to help the field with the rollout of the new standards?

Questions Thank you!!