Glossary of Math Teaching Strategies

Accelerated or individualized math: a system of having students work at different levels individually in one classroom. They progress by passing tests for each unit and move at their own pace.

Adjusted speech: teacher changes speech patterns to increase student comprehension. Includes facing the students, paraphrasing often, clearly indicating most important ideas,limiting asides, etc.

Curriculum Based Probe: having students solve 2-3 sheets of problems in a set amount of time assessing the same skill. Teacher counts the number of correctly written digits,finds the median correct digits per minute and then determines whether the student is at frustration, instructional, or mastery level.

Daily re-looping of previously learned material: A process of always bringing in previously learned material to build on each day so that students have a base knowledge to start with and so that learned structures are constantly reinforced.

Ecological approach/generate data from real life experiences to use in class: involves all aspects of a child’s life, including classroom, family, neighborhood, and community, in teaching the child useful life and educational skills.

Explicit timing: timing math seatwork in 30-minute trials that are used to help students become more automatic in math facts and more proficient in solving problems. Teacher compares correct problem per minute rate. Used to recycle materials and concepts.

Explicit vocabulary building through random recurrent assessments: Using brief assessments to help students build basic subject-specific vocabulary and also gauge student retention of subject-specific vocabulary. This list of teaching strategies and activities was developed out of a focused brainstorming process conducted with general education, special education and English as a Second Language teachers in Minnesota during the 2001-2002 school year. The list represents strategies and activities that teachers report that they use(or have used)to teach middle school-aged English language learners with disabilities. In most cases, the words that the teachers used to describe a strategy or activity are what is presented here in the glossary. A few of the strategies listed have definitions taken from professional literature. In the 2004-2005 school year NCEO will conduct single-case studies with ELLs who have disabilities that will be based on selected strategies from this list.

Graphic organizers: visual displays to organize information into things like trees,flowcharts, webs, etc. They help students to consolidate information into meaningfulwhole and they are used to improve comprehension of stories, organization of writing,and understanding of difficult concepts in word problems.

Model-lead-test strategy instruction (MLT): 3 stage process for teaching students toindependently use learning strategies: 1) teacher models correct use of strategy; 2)teacher leads students to practice correct use; 3) teacher tests’ students’ independent useof it. Once students attain a score of 80% correct on two consecutive tests, instruction onthe strategy stops.

Monitoring of progress through group and individual achievement awareness
charts: Using charts to build awareness and motivation of progress for students. The emphasis here is on progress so even students working at different levels can chartsignificant gains. Native language support: providing auditory or written content input to students in their native language.

Problem solving instruction: explicit instruction in the steps to solving a mathematical or science problem including understanding the question, identifying relevant and irrelevant information, choosing a plan to solve the problem, solving it, and checking answers.

Reciprocal peer tutoring (RPT) to improve math achievement: having students pair,choose a team goal to work toward, tutor each other on math problems, and then individually work a sheet of drill problems. Students get points for correct problems and work toward a goal. Reinforcing math skills through games: Using games to follow-up a lesson in order to reinforce learned skills and use the skills in another context.

Response journal: Students record in a journal what they learned that day or strategies they learned or questions they have. Students can share their ideas in the class, with partners, and with the teacher.

Student developed glossary: Students keep track of key content and concept words and define them in a log or series of worksheets that they keep with their text to refer to.

Students generate word problems: Have students create word problems for a specific math skill. Through the construction of a problem the students learn what to look for when solving word problems they are assigned. Tactile, concrete experiences in math: Using three dimensional objects in math instruction such as geometrical shapes, coins, or blocks used to form various geometrical shapes.

Think-alouds: using explicit explanations of the steps of problem solving through teacher modeling metacognitive thought. Ex: Reading a story aloud and stopping at points to think aloud about reading strategies/processes or, in math, demonstrating the thought process used in problem solving.

References:
Celce-Murcia, M. (Ed.). Teaching English as a second or foreign language. 3rd Ed.
Boston: Heinle & Heinle.
Chamot, A.U. & O’Malley, J.M. (1994). The CALLA handbook: Implementing the
cognitive academic language learning approach. New York: Addison-Wesley.
ERIC Digest. (1993). Teaching limited English proficient students to understand
and use mathematics. ERIC DIGEST 70. (EDO-UD-91-0). Document accessed on the web:
http://eric.web.tc.Columbia.edu/digests/dig70.html on February 23, 2001.
Laturnau, J. (2001, June). Standards-based instruction for English language
learners. PREL Briefing Paper (PB0102). Honolulu, HI: Pacific Resources for Education
and Learning.
Meyen, E.L., Vergason, G.A., & Whelan, R.J. (1996). Strategies for teaching
exceptional children in inclusive settings. Denver: Love Publishing Co.
Rathwon, N. (1999). Effective school interventions: strategies for enhancing
academic achievement and social competence. New York: The Guilford Press NYC.
Smith, T. et al. (1995). Teaching children with special needs in inclusive settings.
Allyn and Bacon.

Math Think-Alouds

Inquiry Based Science

Program Outcomes

For over a year the MAT faculty and staff have been in the process of creating a conceptual framework. The conceptual framework serves as the guiding structure to articulate the multiple dimensions of the MAT teacher education program. The creation of this document consists of multiple steps. Here are some of them:

•Review our mission and vision
•Review our philosophies and goals
•Determine the knowledge bases in the program with regard to theories, research, and practice
•Determine candidate proficiencies
•Align the above with local and national standards
•Determine, select and create assessments.

All of these aspects were discussed among the staff and brought to the faculty for further discussion and analysis. Last summer the faculty and staff worked with well known researcher Marilyn Cochran-Smith from Boston College to further guide, clarify, and validate our work. The process was time consuming, but it was very worthwhile. All of this work has led to a shared vision of the curriculum that is coherent and meaningful.
The most important result that has occurred in this process has been the creation of four program outcomes. It is important for you to get acquainted with them. Please read them and answer the questions below.

I. Candidates have knowledge of diverse learners and are responsive to their developmental and social contexts.
All candidates will:
•design appropriate research-based learning experiences that reflect understanding of developmental stages and the way each student learns;
•develop appropriate learning experiences that reflect an understanding of the language and culture of others;
•establish a safe environment where each student is accepted and where curiosity and risk taking are valued;
•use student’s prior knowledge to make personal connections to subject matter.

II. Candidates have the knowledge of teaching as intricate and collaborative work.
All candidates will:
•set expectations for learning, model learning strategies, and provide constructive feed-back;
•create opportunities for students to self-assess;
•use a variety of explanations and multiple representations of concepts that help students develop conceptual understanding;
•deliver effective instruction based on research to keep students challenged, focused and accountable;
•revise instructional strategies both long range and moment to moment; as necessary;
•use technological advances to enrich instructional practices;
•collaborate and work in partnership with peers, schools, families, other professionals and agencies in supporting student learning.

III. Candidates will know their subject matter and how to teach it in light of the social purposes of education.
All candidates will:
•have a deep understanding of the history, structure and real-world purposes of education;
•use research in the disciplines that they teach.
•incorporate local, state and national standards curriculum and instruction
•balance breadth and depth, incorporate affective and cognitive goals for learning.
•know professional, educational, legal and ethical responsibilities to students and their families.
•teach specific subject matter in ways that are universally accessible to all students.

IV. Teacher candidates will become reflective teacher researchers who will use assessment and contextual data to inform practice.
All candidates will:
•continuously use insights from assessment for instructional and programmatic changes over time;
•design and/or select assessments that embody standards and goals using the backward design process;
•select and/or design tools that are most useful for assessing student competence;
•analyze and synthesize data from multiple sources to identify strengths and needs at the classroom, school and district level to inform instruction;
•provide data-based accommodations and modifications addressing academic and contextual variables that may influence students’ performance.

These outcomes are our beliefs and thus the foundation of the MAT program.

Why do you think we chose these outcomes? What do these mean to you?

Further explanation these ourcomes will occur in later posts.

Outcomes for Teachers