A Guide to Effective Instruction in Mathematics, Volume Five, Teaching Mulitdigit Computations.
- Most students can learn the basic facts accurately, although their speed may vary considerably
- Students should learn the facts in a problem-solving context
- Students should have many experiences modeling the facts using concrete and pictorial representations
- Students should be encouraged to look for pattern and relationships between the operations and number in the facts
- Students need strategies that help them reason their way to the solutions for the facts, rather than strategies for memorizing the facts.
- Student who learn basic facts without understanding them do not know when or how to use what they know. Such learning is often transitory
- Students should not be compelled to memorize facts if they have limited strategies for solving facts. Students who have a repertoire of strategies will be able to find an accurate answer, and over time their speed will naturally increase"
MAKING MATHEMATICS ACCESSIBLE TO ALL
Differentiation and celebration of diversity in key in making Mathematics worthwhile. Differentiation is a teaching skill that is essential in providing an effective Mathematics' program, one that would reach many students with various backgrounds and exceptionalities. Factors to consider are listed below.
4 FACTORS THAT AFFECT LEARNING IN MATHEMATICS
Based on the booklet Teaching and Learning Mathematics: The Report of the Expert Panel on Mathematics in Grades 4-6 in Ontario
Teacher’s | - teaching and learning experiences (background) - teaching and learning style - sensitivity to the students’ needs, learning styles and backgrounds - approaches to teaching (balance between traditional and 3 part lesson) - balanced program in Math- guided, shared and independent Math - organisation and skills in preparing sequential and well scaffolded lessons - attitude towards and knowledge of Math - positive and constructive modeling (as well as modeling and teaching students that it is okay to make mistakes, get messy) - ongoing assessments - collaboration with other teachers |
Student’s | - background (socio-economic situation, gender, language and culture, special needs, limited Math foundation) and prior knowledge - learning style - family circumstances and met basic needs - attitude towards Math - choice to be an active learner versus a passive learner - preconceived notions of Math (i.e., Math is for Math nerds, Math is suppose to be solved quickly, etc.) - peer group influences |
Learning environment | - Safe environment to try new things, make mistakes and not be ridiculed - Seating plans - Flexible groupings - Availabilty of manipulatives to work with - Rich environment filled with Math resources and literature - Math corner with challenges and games, as well as a Math word wall and/or anchor charts - Post metacognitive questions or write them down while they are working. - Technology as a resource - Opportunities to problem-solve and share new ideas/strategies - Differentiated tasks with various entry points - Lessons: cross-curricular, progressive/sequential/cumulative, 3-part structure ensuring students have an opportunity to consolidate - Fun, meaningful problems to solve and to chose from (differentiated and parallel tasks) - Structured and well thought out lesson plan - Clear expectations and goals - Opportunities for Guided, Shared and Independent Math - Celebrate diversity |
Parents’ | - Attitude and knowledge of Math - Involvement in helping his/her child understand Math Big Ideas - Preconceived notions of Math - Positive modeling of perseverance in problem-solving |
EFFECTIVE ACCOMODATIONS BENEFICIAL TO ALL
· Use a problem-based approach with a problem that allows a range of entry points (while considering their prior knowledge and backgrounds)
· Give students a problem that is relevant or that they can relate to
· Form heterogenous groups or groups based on a goal you set out for a specific group of students (flexible grouping)
· Allow students to work by themselves
· Model communication of ideas. Write ideas down on chart paper or the blackboard.
· Tell students that they can use various manipulatives to show their work.
· Tell students what the goal is and what the expectations are
· For ESL students, read the question with the class, and ensure a complete understanding of the question by examining the “math information”
· Provide differentiated and parallel tasks
· Provide a choice activities
· Provide a choice of extended activity for the stronger and quicker students
· Acknowledge all strategies and ah ha moments during the consolidation stage of learning
· Use anchor charts and lots of visuals!
· Accomodate the different learning styles (visual, auditory and kinesthetic learner)
· Use mini whiteboards when in large group activation activities - to allow students to test drive their theory before sharing with the class
· Provide time to think and solve a problem
· Use technology to reinforce concepts learned and increase procedural efficiency
· Get parents involved
Assessment
· Use different ways to assess knowledge and skills (oral interviews, learning logs, more time for completion of tasks, portfolios, etc.)
· Check for students understanding regularly and frequently
· Allow time for students to process the question you asked
· Provide “cloze” activities or “complete the sentence” activities to help the student communicate his/her ideas and thoughts
BARRIERS THAT COULD POTENTIALLY KEEP A CHILD FROM LEARNING
· Teacher’s attitude towards math
· Teacher’s understanding of the big ideas in Math
· Teacher’s willingness and commitment to work with a multidisciplinary team to differentiate task
· Teacher’s ability to provide a rich environment for learning
· Teacher’s ability to provide differentiated tasks
· Teacher’s ability to provide a balanced program
· Teacher’s ability to challenge students metacognitively
· Teacher’s ability to stay organised, assess students regularly, and communicate his/her observations with the parents, as well as to get them involved
· Students’ socio and economic status
· Students’ race
· Students’ needs are not met
· Students’ preconceived notion of Mathematics
· Students’ fears
· Students’ understanding of the problem
· Students’ attitude towards Mathematics
· Parents’ involvement
· Parents’ attitude towards Math
· Parents’ preconceived notion of Math
· The learning environment: safe atmosphere, clear goals and expectations, richness of the classroom resources and literature, visuals, anchor chart, choices, differentiated and meaningful problems, availability of technology, school funding.
Research have indicated that one's race and income affects one's achievement (http://media.curriculum.org/curriculum/CSC256OERP/EN/10GRashtiWMartino.wmv ). This is also witnessed in my classroom. Many of my students' families are from low socio-economic backgrounds; many are ESL or ELL students who live in a family who struggles financially.
ACCOMODATIONS FOR SUPPORTING LOW INCOME AND/OR ESL/ELL STUDENTS
(With reference to the book “Many Roots Many Voices: Supporting English language learners in every classroom; A practical guide for
FOR LOW INCOME STUDENTS
· Provide food through a school breakfast program
· Ask students to bring in school donations of clothes for the less fortunate
· Have a snack bin where students can exchange their junkfoods for healthier foods
· Have them involved as much as possible in their school community
· Provide homework clubs
· Get them hooked up with the Big Brothers and Sisters program within their community
· Form support groups for high risk students
· Praise all accomplishments to build self-esteem
· Provide a safe and positive learning environment with many resources, manipulatives to work with
· Provide differentiated tasks and choices in activities
· Set realistic goals and hold high expectations
· Provide parents with tips on how to help their children at home (i.e., homework – literacy and numeracy)
FOR ESL/ELL STUDENTS AND/OR LOW INCOME STUDENTS
· Be familiar with the ESL/ELL stage of development
· Assess their prior knowledge (Give the student a variety of Math concepts and strategies and ask him/her which ones they are familiar with)
· Use their background, knowledge and skills to enrich our lessons
· Engage learners in activities that appeal to their interests and build on their existing knowledge, skills and backgrounds
· Relate mathematics to real-life experiences
· Use mathematics as a tools for developing the learning community
· Modify some or all curriculum expectations
· Assign tasks that are appropriate to the student’s level of proficiency in English
· Teach and model basic vocabulary (avoid idioms and jargon)
· Use questions to help students develop language and concepts of mathematics
· Explicitly teach the vocabulary of mathematics using questions to help students develop the language and concepts of mathematics.
· Ensure that your instructions and expectations are clear (explain homonyms when necessary)
· Simplify language
· Speak clearly- articulating your words and pause often
· Repeat instructions
· Use a variety of visuals, manipulatives, charts, pictures, diagrams and graphic organizers
· Use gestures
· Print key words and instructions
· Write key ideas down or have a scribe for ESL/ELL students
· Encourage peer tutoring and class discussion
· Integrate as many Math words as possible in other subject areas or any community/school event
· Pair the student up with a another student who speaks the same language
· Teach and model to English-speaking students ways they can help English language learners
· Communicate positive feedback about language learning
· Communicate positive attitudes towards newcomers and their cultures
· Provide positive feedback on student effort
· Establish a safe, respectful and supportive environment, where errors are accepted as a normal part of the learning process.
· Work with a multidisciplinary team ( ESL/ELD teacher; board resource staff; MLO; school administration, and all who are involved in this child’s education) - set regular meetings where the homeroom teachers and special education teachers gather together and learn how to examine student work, looking at strengths and possible misunderstanding and misconceptions, examining the key goals and ideas we want students to master and generate questions that could challenge students to deepen their understanding of a specific concept - while ensuring that the student needs match the learning Math goals].
