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Mathematics Now!™
Targeted Assistance for Elementary and Middle Schools
Improving student performance in mathematics requires that we equip elementary and middle school teachers with the knowledge and skills to teach mathematics in more rigorous ways. In fact, the recent report by the National Academy of Sciences (NAS), Rising above the Gathering Storm, bolstered our national priority to provide students a firm grounding in mathematics and science.
Modern Red SchoolHouse (MRSH) meets this challenge by engaging teachers in research-based methods that support how students learn mathematics, including the role of prior knowledge and misconceptions, and how students progress through the three modes of learning described by Bruner.
Mathematics Now! ™ training consists of three modules:
Mathematics Now! ™ Institutes are typically three days with follow-up coaching in the classroom and are customized for individual district needs.
How Students Learn Mathematics
Through interactive methods such as video cases and classroom transcripts, teachers learn to apply the attributes of how students learn to seven critical actions necessary for effective learning in the mathematics classroom. For example, teachers will identify specific misconceptions students have within the various strands of mathematics and strategies for helping students construct accurate understandings. Facilitators guide participants to apply the critical actions to lesson planning during the sessions.
The MRSH Critical Actions are:
- Develop a classroom culture where questioning, respect, and risk-taking are encouraged;
- Engage students’ interests and make connections to the outside world ;
- Integrate new learning with students’ prior understandings;
- Uncover students’ misconceptions and construct accurate understandings;
- Provide the larger landscape of knowledge into which a given concept fits;
- Establish opportunities for students to organize, experience, and apply new concepts; and
- Cultivate students’ use of metacognitive strategies and commitment to excellence.
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Three Modes of Mathematics Learning
The second method of effective mathematics practices relies on the framework of Jerome Bruner, to help students progress through three modes of mathematics learning. Teachers learn how to introduce mathematical concepts in the enactive mode where students use manipulatives to represent visually important mathematics concepts. At this hands-on stage, teachers learn how to move students to a more iconic mode where students draw pictures of the various concrete models they have used and also other more abstract visual representations. Finally, teachers help their students move to a symbolic mode where they use traditional notations and representations. By having students move through all three phases, rather than jumping directly to the symbolic mode, students are able to construct their own understandings and have a more solid conceptual base of knowledge.
At all times in this process, teachers are encouraged to understand multiple representations of information (e.g., algebraic and graphical representations of functions), to make connections both within strands of mathematics and between mathematics and other disciplines, and to communicate mathematical information in effective ways. Rigorous problem-solving, using tasks which are challenging, open-ended, and have multiple possible approaches, is incorporated into inquiry-driven sessions. Reasoning and proof, as in an explanation of why a response is reasonable, is a continuing part of the conversation.
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Instructional Coaching in the Mathematics Classroom
In order for teachers to transfer learning to the classroom, they, like their students, need opportunities to reflect on new learning in the context of their own classrooms. The third part of learning effective mathematical practices involves instructional coaching, a cycle of collaborative planning between teacher and coach, model teaching, observations, and feedback. Instructional coaching provides contextualized, ongoing, professional development for elementary and middle school teachers as they improve their teaching of mathematics.
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Resources
Mathematics Now! ™ training is based upon principles of practice that have been established in scientific research. Resources for the development of the training include:
Bransford, J.D., and S. Donovan (eds). 2005. How Students Learn. Washington, DC: National Academies Press.
National Academy of Sciences. 2006. Rising above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future . Washington, DC: National Academies Press.
National Council of Teachers of Mathematics. 2000. Principles and Standards for School Mathematics. Reston, VA: NCTM.
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