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http://sim.abel.yorku.ca @LNSSIM #WINTERSIM #SIMK12 System Implementation and Monitoring Regional Session Winter, 2015 Welcome and Agenda Morning Tasks in Mathematics Classrooms Afternoon Sharing of Implementation Steps and Monitoring Actions in Like-Role Groups TWEET WITH US #WINTERSIM #SIMK12 @ LNSSIM Determine where you might be in Ontario given the information in the chart below. Think on your own for 5 minutes. City Distance as bird flies (km) Driving Distance (km) Windsor Toronto Ottawa Thunder Bay Niagara Falls North Bay 454 398 549 544 463 245 763 540 647 902 653 289 City Windsor Toronto Ottawa Thunder Bay Niagara Falls North Bay Distance as bird flies (km) 454 398 549 544 463 245 Driving Distance (km) 763 540 647 902 653 289 Determine where you might be in Ontario given the information in the chart below. Think on your own for 5 minutes. This is an example of a contextual mathematics task. Best Evidence Synthesis on Effective Pedagogy in Mathematics Effective mathematical pedagogy is a coherent system rather than a set of discrete, interchangeable strategies. This pedagogical system encompasses: • A non-threatening classroom environment • Instructional tasks • Tools and representations • Classroom discourse Effective Pedagogy in Mathematics/Pangarau by Glenda Anthony & Margaret Walshaw, New Zealand (2007) Quality Instruction in a Math Class You have a representative sample of your thinking about quality instruction in mathematics grouped according to the four components of an effective pedagogical system in mathematics. Review and discuss any observations that you have. The Learner Discuss at your tables what the student should be able to do if there is quality instruction. What is the image of the mathematics learner that emerges if the four components of the pedagogical system are evident? Effective Teaching and Learning The learning of mathematics has been defined to include the development of five interrelated proficiencies that, together, constitute mathematical proficiency (NRC 2001): • Conceptual understanding • Procedural fluency • Strategic competence • Adaptive reasoning • Productive disposition Posing Worthwhile Mathematical Tasks “It is through tasks that the curriculum and the discipline of mathematics comes alive. Starting with students’ prior knowledge and then creating rich, mathematical tasks, teachers help students to proceed gradually from their informal knowledge of the ideas in the domain to more formal notions.” (Romberg and Kaput, 1999) Posing Worthwhile Mathematical Tasks “Tasks should be created or selected that have the potential to encourage students to wonder why things are, to inquire, to search for solutions and to resolve incongruities”. (Hiebert et al. 1996) Rich Tasks What is also apparent to me is that much of what it takes to make a rich task “rich” is the environment in which it is presented, which includes the support and questioning that is used by the teacher and the roles the learners are encouraged to adopt. That is, an environment in which learners are not passive recipients of knowledge, accepting what is given, but independent assertive constructors of their own understanding, who challenge and reflect. On its own a rich task is not rich – it is only what is made of it that allows it to fulfil its potential. Jennifer Piggot http://nrich.maths.org/5662 “On its own a rich task is not rich – it is only what is made of it that allows it to fulfil its potential”. Jennifer Piggott http://nrich.maths.org/5662 Time for Chocolate! Chocolate Bar Task • This is an example of a purposeful representative task • These tasks are usually not “contextualized”, however there was sometimes a hook to engage students • While the mathematics may be explicit, extensive exposition by the teacher is not necessary as the provision of the model or representation enables the students to generate the mathematical ideas and justification. • The model, representation, or tool is ideally closely linked to the mathematical concept being developed, in order to be effective. Types of Mathematics Tasks In studies of mathematics tasks, four general types have been identified: Purposeful representative tasks Contextual tasks Contentspecific tasks Practice and consolidation tasks Purposeful representative tasks Contextual tasks Contentspecific tasks Practice and consolidation tasks Content-Specific Task If the perimeter of a rectangle is 64 m what might be the area? Purposeful representative tasks Contextual tasks Contentspecific tasks Practice and consolidation tasks Content-Specific Task • Often an open task • Although, the student needs specific content knowledge to solve • Involves investigating, creating, communicating, generalizing and coming to know procedures Purposeful representative tasks Contextual tasks Contentspecific tasks Practice and consolidation tasks Practice and Consolidation Tasks Factor the expression x 2+ 5x + 6 = 0 Find the value of ½+¾ • Are an important part of a balanced mathematics program • Provide students with opportunities to solidify mathematical concepts and procedures • Provide independent practice DOG PEN How Tasks Contribute To Students’ Mathematical Proficiency Type of Task Purposeful Representative Mathematical Proficiency Conceptual Understanding Mathematical Fluency Contextual Content-specific Strategic competence Adaptive reasoning Strategic competence Adaptive reasoning It is understood that there can .be overlap of proficiencies across various tasks. These are the main ones that are developed. P. Sullivan et al. Teaching with Tasks for Effective Mathematics Learning. • This is one way to monitor the effectiveness of the mathematics teaching and learning in your system • It is one component of the pedagogical system; however as many researchers have argued it is a critical element • Even though looking at tasks without student thinking and/or work has limitations, it does give us a window into the mathematics that students experience in our classrooms Conversation Tool for Reflection on Mathematical Tasks Conversation Tool for Reflection on Mathematical Tasks Grade Groups Each grade group will collaboratively discuss a selection of mathematical tasks. The Conversation tool has been designed as a starting point for your discussion. Think about the collection of tasks to see if there is a sampling of the four types: contextual, purposeful representative, content-specific and practice/consolidation. K-2 3-5 6-8 9-12 Grade Groups and Rooms TASK 6-8 K-2 3-5 9-12 ROOM Venetian Castelli AB Castelli C Dolce 12:00 – 12:45 Board Teams Analyze the tasks that you brought using the conversation tool. Cross-Board Like-Role Sharing ROLE Principal/ Vice-Principal Consultant/Co-ordinator/ Teacher Superintendent ROOM Venetian Castelli AB Castelli C Feedback Survey Complete your feedback survey Your feedback is important to us! See you at the Spring 2015 SIM K-12! DOG PEN