Chapter 6: Planning: A Framework for
Differentiating

In planning for math, the authors suggest that teachers map out the curriculum for the school year in
chunks, aligned with the academic schedule. Major units should have key deadlines for beginning
and ending...these dates may change, but they provide a target for the year. The authors give a specific example of the plan for a combined seventh and eight
grade math class, which is designed around the trimesters they have.

The overall planning is first done by
trimester, broken down by month (for me this would be by quarters). The next step is to plan the first unit, while
looking at the school calendar. They use a 3-column planner – the first column
lists the days/dates of math classes. The second column lists what part of the
unit is planned for each day. The third column is to track the progress made
each day. After the weekly planning for the unit is complete, daily planning
should occur.

The authors discuss Bloom’s Taxonomy and
its revision to the four dimensions of knowledge (factual, conceptual,
procedural, and metacognitive) with six levels of cognitive processing for each
dimension (remember, understand, apply, analyze, evaluate, and create). The authors set these up in a chart, with the
four dimensions along the left side and the six levels of processing along the
top. This is to provide a visual to help
design lessons and activities when planning.

Something to consider in planning is
that all math concepts have three components of learning: the language associated with the concept, the
conceptual understanding, and the skills and procedures connected to the
concept. Students need to have strong
language and conceptual foundations when learning math concepts – rather than
simply memorizing facts or procedures.

Prerequisite support skills for learning math, identified by Mahesh Sharma are “nonmathematical skills” that are needed for math conceptualization. They include: sequencing, classification, spatial orientation, estimation, patterns, visualization, deductive thinking and inductive thinking. The authors state that these skills need to be incorporated in the planning process and should be part of differentiation.

The authors state that daily routine is important, and that an hour for
math class is ideal (I have about 40 minutes). The daily routine the authors recommend
is:

* beginnings (warm-ups)

* homework processing

* minilesson and launch

* exploration

* summary

* homework assignment and daily reflection.

* beginnings (warm-ups)

* homework processing

* minilesson and launch

* exploration

* summary

* homework assignment and daily reflection.

To differentiate during the warm-ups, different students can work on
different problems; students could create warm-ups, have students describe strategies
to build language.

Homework processing can be done in small groups, with students
comparing answers, and then teacher selecting items for discussion. To
differentiate in homework processing, the authors suggest organizing the groups
by differentiated homework tasks or choosing discussion problems that allow
for intervention opportunity with specific students.

The minilesson is the part of the lesson that focuses on the objectives
for the day. “Launching” the minilesson includes connecting to previous work,
discussing the math language and setting the context. If the teacher is aware of gaps, this is the time to address those
needs. To differentiate at this point, the authors suggest selecting students to
respond based on prior experience and assessments, design participation that
reflects needs of various intelligences; include prerequisite skills practice;
use think-pair-share; introduce tiered tasks.

During the exploration part of the lesson students work on assigned
tasks with partners, groups, or individually. The teacher monitors,
conferences, observes, supports, redirects, and asks probing questions.
Students who finish tasks early are to work on the anchor activities. This is
the time of greatest differentiation: students work in their own ways, at their
readiness levels, with tasks designed for their needs, and students use anchor
activities. During this time, the teacher lets the students do the work – lets
them struggle some (not to frustration/upset level), make mistakes, and analyze
their errors.

Class summary, in the authors’ view, is the most critical part of the
lesson. This is the time to refocus the class on the math and “consolidate” the
learning. The teacher facilitates the discussion, selects the order of sharing,
asks for thinking and reasoning, questions, patterns, generalizations,
etc. If the lesson is not actually “finished”
at the end of math time (which happen to me quite often, with only 40
minutes!), then the summary should be a “status of the class” summary to
prepare for the next class period. Differentiation during this time is the sharing of thinking, reasoning,
showing evidence, making connections, testing new ideas – not about sharing “right”
answers.

Homework and Reflection is recommended to be the last five minutes of
class. After recording their homework assignment and asking any questions about
it, students are asked to write a summary of the math they worked on during the
period and record any questions they have. Prepared Exit Slips, which could be
more specific to the day’s content, could also be used at this time. Differentiation
during homework assignment would be assigning different homework to particular students
based upon need.

I love the concept of the lesson structure presented here. As the authors stated, an hour for math is
ideal, but I only have 40 minutes. I need to find a way to make this structure
work…..I think about doing half of the lesson each day, which would put some
exploration on day 1 and some on day 2.
Then, would it be appropriate to give homework and do homework processing each day? Or should there
not be homework on day 1 of the lesson? I need to brainstorm. Anyone have ideas?