Math workshop for primary teachers

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Math workshop for primary teachers

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2. The concept of big ideas requires students to understand basic concepts. Develop inquiry and problem solving skills and connect these concepts and skills to the real life situation. BIG IDEAS 3. "Big ideas are really just large networks of interrelated concepts...whole chunks of information store and retrieved as single entities rather than isolated bits." (Van de Walle, 2001). MORE ON BIG IDEAS 4. Big ideas need to be explicitly described and modeled by the teacher, and students need time to actively manipulate the information and to discuss and reflect with one another on the big ideas and the knowledge and skills along with those principles The big ideas in Geometry and Spatial Sense are: Properties of two-dimensional shapes and three dimensional figure Geometric relationships Location and movement EXAMPLE OF BIG IDEAS 5. Helping children see, hear, and feel mathematics Displaying and encouraging positive attitudes towards mathematics Making resources available Encouraging connections of various kinds Valuing prior knowledge Making meaningful home connections Focusing on the big ideas of mathematics PROBLEM SOLVING APPROACH TO UNDERSTAND BIG IDEAS 6. A balance of shared guided and independent learning set in a supportive and stimulating environment. PROBLEM SOLVING AND CLASS ROOM STRUCTURE 7. a visible mathematics area in the room where core manipulatives are kept; manipulatives accessible to children throughout the day as needed, with routines established for their distribution and collection; manipulative storage bins or containers that are labelled for easy identification and clean-up; mathematical reference materials that are displayed around the room (e.g., calendar, number lines, hundreds charts); computers that are accessible to all children; areas for instructional groupings (whole group, small group, individuals). CLASS ROOM STRUCTURE FOR PROBLEM SOLVING APPROACH IN MATHEMATICS BIG IDEA LEARNING 8. promote mathematical tasks that are worth talking about; model how to think aloud, and demonstrate how such thinking aloud is reflected in oral dialogue or in written, pictorial, or graphic representations; encourage students to think aloud. This process of talking should always precede a written strategy and should be an integral component of the conclusion of a lesson; model correct mathematics language forms (e.g., line of symmetry) and vocabulary; encourage talk at each stage of the problem-solving process. Students can talk with a partner, in a group, in the whole class, or with the teacher; ask good questions and encourage students to ask themselves those kinds of questions; ask students open-ended questions relating to specific topics or information; COMMUNICATION IN PROBLEM SOLVING 9. encourage talk at each stage of the problem-solving process. Students can talk with a partner, in a group, in the whole class, or with the teacher; ask good questions and encourage students to ask themselves those kinds of questions; ask students open-ended questions relating to specific topics or information; encourage students to ask questions and seek clarification when they are unsure or do not understand something; provide wait time after asking questions, to allow students time to formulate a response COMMUNICATION.CONT. 10. pair an English language learner with a peer who speaks the same first language and also speaks English, and allow the students to converse about mathematical ideas in their first language; model the ways in which questions can be answered; make the language explicit by discussing and listing questions that help students think about and understand the mathematics they are using; give immediate feedback when students ask questions or provide explanations; encourage students to elaborate on their answer by saying, Tell us more; ask if there is more than one solution, strategy, or explanation; ask the question How do you know? Writing and talking are ways that learners can make their mathematical thinking visible. (Whitin & Whitin, 2000, p. 2) MORE ON COMMUNICATION 11. Observation Interviews Conference Portfolio Tasks and daily work Journals and logs Self -assessment HOW TO ASSESS STUDENTS AS THEY PROBLEM SOLVE 12. Observation is probably the most important method for gaining assessment information about young students as they work and interact in the classroom. Teachers should focus their observation on specific skills, concepts, or characteristics, and should record their observations by using anecdotal notes or other appropriate recording devices OBSERVATION 13. Interviews are an effective tool for gathering information about young childrens mathematical thinking, understanding, and skills. Interviews can be formal (Nantais, 1989) or informal, and are focused on a specific task or learning experience. Interviews include a planned series of questions, and these questions and responses give teachers information about attitudes, skills, concepts, and/or procedures. According to Stigler (1988): INTERVIEWS 14. Conferences/Conversations A conference is useful for gathering information about a students general progress and for suggesting some direction. A conference or conversation might occur in a one-to-one teaching situation or informally as a teacher walks around the room while students are engaged in solving problems. A student-led conference, in which students share their portfolios or other evidence of learning with parents or teachers, is an effective way of helping children articulate their own learning and establish new goals. CONFERENCES/CONVERSATIONS 15. A portfolio is a purposeful collection of samples of a childs work. These samples could include paper-and-pencil tasks, models, photographs of the student at work, drawings, journal entries, or other evidences of learning. This work is selected by the child and includes a reflective component that allows the child to connect with his or her own learning. Portfolios help to monitor growth over time (Jalbert, 1997; Stenmark, 1991). Portfolio assessment allows all learners to show what they know and can do. A variety of formats can be used, from a simple folder to a classroom portfolio treasure chest to document the classs mathematical growth. PORTFOLIO 16. Daily classroom work provides an opportunity for immediate feedback and remediation. This instantaneous reflection by teachers allows them opportunities for making immediate accommodations to their programs. TASKS AND DAILY WORK 17. Journals allow students to share what they know about a mathematical concept. Mathematics journals can include written work, diagrams, drawings, stamps, stickers, charts, or other methods of representing mathematics. Journals also offer students the opportunity to describe how they feel about mathematics or about themselves as mathematics learners. It is important to consider the importance of oral sharing and the modelling of oral communication, which provides scaffolding for young children who are not always able to communicate all their ideas in written form. Journals for young children could be done orally with a tape recorder or as part of an interview JOURNALS AND LOGS 18. Students need opportunities for self-reflection to think and talk about their learning. SELF ASSESSMENT 19. Getting started---------The teacher prepares the grade2 students for a problem., by asking question. Like,have you ever been to a grocery store. Have you ever got free samples. Why they give frees samples.may students reply ..for trying and to buy afterwards. Today lets pretend you are the boss of the grocery store and you have 20 samples of mini packs of cookies. If you give one to each person .how many of people will get the samples.. Answer could be 20 people HOW TO USE PROBLEM SOLVING PROCESS IN THE CLASS ROOM 20. But as a boss you feel that one sample is not enough .you want to give more samples 3 or 4. Look at the problem now how many people will get sample cookies ,if given 3 or 4. Teacher says .you can use counters ,cubes, can have a partner ,can use diagrams ,picture as ur strategies. CONTINUED.. 21. Teacher encourages them to explore and apply strategies that make sense to them . Use number 3 Say3+3+3+3+3+3=18 2 left overs Why left over 3 is..odd number 20 iseven number Show in written work WORK ON IT 22. Share strategies with class student may say they use 20 cubes divided them in group of 4 How many groups5 people will get samples with no left over Counting by 4,8,12,16,20 five people will get samples. Counting by 3,6,9,12,15,18,20.. Six people will samples. What do you recommend 4each or 3 each..big idea is division. Do we have left over during division or unequal on and so far just an example. REFLECTING AND CONNECTING