What does it mean to be a PRINCIPLED mathematics student? What does it mean to be a THINKER in mathematics? PYP > How children learn mathematics cycle What does it mean? What does is look like? Constructing meaning Tuning In / Finding Out The learning outcomes identified in the constructing meaning stage strongly emphasize the need for students to develop understanding of mathematical concepts in order to provide them with a secure base for further learning. Prior Knowledge – students exploring and communicating own personal understandings and knowledge e.g. via a graphic organizer Transferring meaning into symbols Sorting Out The learning outcomes in the transferring meaning into symbols stage are more obviously demonstrable and observable. The expectation for students working in this stage is that they have demonstrated understanding of the underlying concepts before being asked to transfer this meaning into symbols Transfer of understanding into symbolic notation - can take the form of pictures, diagrams, modelling with concrete objects, mathematical notation.
My groups remain stable for long periods of time. My groups change often, with students moving in and out as necessary. All students cover the curriculum at the same speed. The pace of instruction is varied. All students complete the same activities. Students have chances to make choices about activities. I use a small range of instructional strategies. I use a variety of instructional strategies. All students complete all activities. Students complete different activities based on needs. Advanced students are given more content or skills application. Advanced students are given more complex tasks. I assess student learning at the end of the unit. I assess student learning throughout the unit. I usually assess all students in the same way. I allow students to show learning in a variety of ways. I plan one set of learning engagements at the beginning of the unit. I plan for differentiation before beginning a unit. Adapted from Differentiated Instruction in the Regular Classroom: How to Reach and Teach All Learners, Grades 3-12 by Diane Heacox.
Communication Traditional Approach Exploring Inquiry Transitioning to Inquiry Practicing Inquiry Teacher rarely allows student to share information with each other through discussions and dialogue. Teacher occasionally allows students to share information with each other through small group discussions and dialogue. Teacher frequently expects students to share information with each other through small group discussions and dialogue. Teacher consistently expects students to share information with each other through small group discussions and dialogue. Teacher speaks mainly from the front of the room. Teacher usually speaks from the front of the room and occasionally moves about. Teacher frequently moves about the room speaking from different areas. Teacher effectively moves about the room, speaking from different areas to monitor and enhance learning. Teacher communicates by standing above or over students. Teacher occasionally communicates to students by kneeling by or sitting on a student seat to make eye level contact. Teacher frequently communicates to students by kneeling by or sitting on a student seat to make eye level. Teacher consistently communicates to students by kneeling by or sitting on a student seat to make eye level contact. Teacher provides little positive reinforcement. Teacher provides occasional positive reinforcement. Teacher provides frequent positive reinforcement. Teacher provides frequent and equitable positive reinforcement. Communication is mostly from teacher to student and rarely from student to student. Communication is usually from teacher to student by occasionally from student to student. Communication is occasionally from teacher to student but frequently from student to student. Communication effectively varies from teacher to student and from student to student according to the situation. Engagement of Students Teacher engages students through oral questioning and discussion. Teacher engages students through oral discussion and questions. Teacher engages students through open-ended discussions and investigations. Teacher engages students through open-ended discussions, investigations, and reflections. Students are mostly passive but teacher uses some hands-on activities. Students are occasionally active; teacher uses hands-on activities but attempts some open-ended investigations. Students are mostly active; teacher uses hands-on activities but attempts open-ended investigations and encourages explorations. Students are consistently active; teacher use hands-on and minds-on activities that encourage student initiated investigations and explorations. Teacher rarely solicits information from the students. Teacher occasionally solicits information from the students. Teacher frequently solicits information from the students. Teacher frequently and effectively solicits information from the students. Classroom Organization Traditional Approach Exploring Inquiry Transitioning to Inquiry Practicing Inquiry Student desks are Student desks are Student desks are Teacher and students
wait time strategies. uses wait time strategies. uses wait time strategies. and effectively uses wait time strategies. Teacher provides answers when students cannot answer questions. Teacher attempts rephrasing techniques when students cannot answer questions. Teacher frequently uses prompts and rephrasing techniques when students cannot answer questions. Teacher consistently and effectively uses prompts and rephrasing techniques when students cannot answer questions. Assessment Procedures Teacher frequently uses worksheets to assess learning; students record learning on teacher designed sheets. Teacher reduces the use of worksheets to assess learning; teacher attempts having students record on student designed sheets. Teacher seldom uses worksheets to assess learning; students record on student designed sheets and/or journal with some success. Teacher seldom uses worksheets to assess learning; students record on student designed sheets and/or journal with complete success. Teacher mostly uses objective-type testing. Teacher uses objective testing and attempts to implement authentic assessment. Teacher varies assessments to include objective testing, portfolios, rubrics, and other authentic assessments. Teacher consistently and effectively varies assessments to include objective testing, portfolios, rubrics, and other authentic assessments. Teacher assesses students based on content information only. Teacher assesses students based on content and skills. Teacher assesses students based on content, skills and problem-solving skills. Teacher assesses students based on concepts, knowledge, attitudes, transdisciplinary skills and action taken because of new learning. Teacher works as an individual. Teacher works with another teacher to share inquiry strategies and activities. Teacher works in collaboration with others to develop and share inquiry strategies. Teacher works in collaboration with others in study group sessions to share units, articles and success stories. Reference: Adapted from Inquire Within, D. Llewellyn