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Inside Mathematics Frequently Used Terms and Concepts

Mathematics Assessment Resource Service (MARS)

This international initiative has intensively partnered with districts and states around the design of balanced tasks for formative and summative assessment of student mathematics learning. The tasks available in Tools for Educators were developed by the MARS initiative.

To learn more about the MARS work and outcomes, visit http://www.nottingham.ac.uk/~ttzedweb/MARS/.

Mathematics Coaching

Many of the professional conversations on this website involve the coaching model of professional learning in mathematics teaching. The coaches are all highly accomplished and experienced classroom teachers who have chosen to assume a mentoring role. There are multiple models of coaching visible in the classroom visits on this website, which include:

  • One-on-one planning, observing and debriefing
  • Teacher cohort facilitation and leadership
  • Classroom observation and support

The educators involved in coaching roles also discuss the challenges of their work in Tours of Inside Mathematics.

Public Lessons, or Lesson Study

The documented classroom visits in this website share lessons developed in a cohort, collaborative model inspired by the Japanese tradition of "lesson study." In the lesson study model, faculty work together intensively to craft, observe, refine, and polish lessons for student learning. Commonly, the development faculty cohort all come to observe the lesson being taught, take detailed notes (each perhaps focusing on a pair or small group of students), and share their observations with each other in a debrief conversation.

To learn more about lesson study, visit http://www.tc.edu/lessonstudy/lessonstudy.html.


Many of the teachers on this website refer to using the MARS tasks for the purposes of "re-engaging" their students in an analysis of effective and ineffective solving strategies. Generally, this process involves:

  • The teacher administers the task or assessment in her classroom
  • She or he then gathers all the student work and conducts a close reading of responses to identify diverse successful strategies as well as trends in student misconceptions
  • The teacher then removes extraneous or distracting information from selected examples of student work, and shares them with the class in a sequenced manner, asking students, "What was this student's approach? What do you think he or she was trying to accomplish? How effective was it? What advice would you give this student?"

To learn more about the strategy of re-engagement, see Improving Our Craft as Coaches and Reflection-Observation.

Silicon Valley Mathematics Initiative (SVMI) and First In Math Consortium (FiMC)

The Silicon Valley Mathematics Initiative is a comprehensive effort to improve mathematics instruction and student learning in a large number of Silicon Valley schools and then to broadly disseminate the learning. The Initiative was based on two central beliefs or theories of action:

  • Positive change is education that occurs through a continuous loop of focusing on high standards, assessing students' work to the standards, examining students' products and analyzing students' understandings from the assessments, developing effective educational strategies and practices that are consistent with the findings, and tailoring instruction to enhance student learning and understanding
  • Improved achievement is an outcome of improved instruction. Improved instruction is an outcome of ongoing, comprehensive, intensive professional development based on high performance expectations, ongoing professional development and improved math instruction

To learn more about SVMI's ongoing work visit http://www.svmimac.org/.

The First in Math Consortium (FiMC) provided professional development and technical support for key role groups from each of the districts - superintendents and curriculum & instruction leaders, principals, coaches, and math teachers. District teams came together periodically to report progress, discuss challenges, and plan next steps. Middle school and K-8 principals participated in professional development sessions during the year. The project supported middle school teachers in improving their content knowledge and instructional strategies for teaching algebra. Math coaches also participated in ongoing professional development sessions focused on content, pedagogy, and coaching strategies with teacher teams. A major focus was the formation of professional learning communities in middle school math departments. To learn more about FiMC, visit http://www.noycefdn.org/fimc.php.


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