A description of the course offered by the Massachusetts Department of Education and Teachers 21.

1. Developing
Mathematical
Practices
Number, Operations, and Algebraic Reasoning
K-5

2. Course Overview
Participants in the course will:
Reflect upon the standards for mathematical
practice as outlined in the CCSS.
Explore content standards in Number,
Operations, and Algebra

3. Selected Standards
for Mathematical
Practice
Make sense of problems and persevere in
solving them
Reason abstractly and quantitatively
Construct viable arguments and critique
the reasoning of others
Look for and make use of structure

4. A deep appreciation of the
mathematical standards will
be achieved through:
solving non-routine problems
exploring alternative algorithms
asking, “does my answer make sense?”
decontextualizing and contextualizing
making conjectures and using
counterexamples
communicating one’s reasoning
viewing complicated things as single
objects
using properties of numbers and equality

5. Specific Content
Areas To Explore:
base 10 place value
other number bases
comparing and ordering fractions
alternative strategies for fraction
operations
solving linear equations using non
traditional models

6. Pedagogical Skills
Will Be Strengthened
by:
individual and group problem solving
cooperative learning strategies
cultivating norms of collaboration
playing games to build reasoning and communication skills
promoting classroom discourse
looking at the MPs in action: classroom videos
using technology to share resources and collaborate
taking part in roundabout and station activities
using activators, summarizers, text protocols
the benefits of recreational math to build perseverance
differentiated math instruction
the use of assessment tasks to design effective instruction

7. Final Course Project
By designing and carrying out a final project, participants will:
deepen understanding of the mathematical practice
standards
support students in becoming more competent problem
solvers
engage student participation around a particular math
practice
write a lesson plan highlighting number, operations or algebra
content from the course
describe formative and other assessments
collect and analyze student work
include a short video clip of students making use of the math
practice standard(s)
• include annotated versions of the lesson plan by
incorporating changes made after instruction