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System Implementation and Monitoring
Regional Session
Winter, 2015
Resources are available at
sim.abel.yorku.ca
Tasks in Mathematics Classrooms
Sharing of Implementation Steps and
Monitoring Actions in Like-Role Groups
Welcome and AgendaMorning
Afternoon
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 454 763Toronto 398 540Ottawa 549 647Thunder Bay 544 902Niagara Falls 463 653North Bay 245 289
City Distance as bird flies (km)
Driving Distance (km)
Windsor 454 763Toronto 398 540Ottawa 549 647Thunder Bay 544 902Niagara Falls 463 653North Bay 245 289
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 LearnerDiscuss at your tables what the student would demonstrate 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?
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
Effective Teaching and Learning
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)
Insert video of Lucy West here.
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 Piggott 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 is 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.
Purposeful representative tasks
Contextual tasks
Content-specific tasks
Practice and consolidation tasks
In studies of mathematics tasks, four general types have been identified:
Types of Mathematics Tasks
Content-Specific Task
If the perimeter of a rectangle is 64 m what might be the area?
Purposeful representative tasks
Contextual tasks
Content-specific tasks
Practice and consolidation tasks
Content-Specific TaskPurposeful representative tasks
Contextual tasks
Content-specific tasks
Practice and consolidation tasks
• Often an open task
• Although, the student needs specific content knowledge to solve
• Involves investigating, creating, communicating, generalizing and coming to know procedures
DOG PEN
Practice and Consolidation Tasks
Factor the expression x + 5x + 6 = 0
Find the value of
½ + ¾
Purposeful representative tasks
Contextual tasks
Content-specific tasks
Practice and consolidation tasks
2
• Are an important part of a balanced mathematics program
• Provide students with opportunities to solidify mathematical concepts and procedures
• Provide independent practice
Strategic competence Adaptive reasoning
Purposeful Representative
.
How Tasks Contribute To Students’ Mathematical Proficiency
Mathematical Fluency
Contextual
Content-specific 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.
Conceptual Understanding
Type of Task Mathematical Proficiency
Strategic competence Adaptive reasoning
Purposeful Representative
.
How Tasks Contribute To Students’ Mathematical Proficiency
Mathematical Fluency
Contextual
Content-specific 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.
Conceptual Understanding
Type of Task Mathematical Proficiency
• 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
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.
Grade Groups K-2, 3-5, 6-8, 9-12
K-23-5 6-8
9-12
Grade Groups and Rooms
TASK ROOM
K - 2 Kensington 1
3 - 5 Kensington 2
6 - 8 Manchester
9 - 12 London A
12:00-12:45
Board Teams
Analyze the tasks that you brought using the conversation tool.
Insert video of Superintendent Observations here
Insert Video of Principal as Co-Learner here.
Cross-Board Like-Role Sharing- strategy
-how did you monitor it?-what did you learn?
ROLE ROOMSuperintendent Bristol Principal / Vice Principal Kensington 1Principal / Vice Principal Kensington 2Program Staff /Teacher ManchesterProgram Staff /Teacher London A
Spring SIM
There will be like-role, cross board sharing again but you will need 2 pieces of evidence.If you are an SO you will need evidence of your new learning and evidence of what the principals in your FOS have learned. If you are a principal you bring evidence of your learning and the learning of your teachers.If you are program staff, bring evidence of your learning and the learning of educators you work with.
YOUR FEEDBACK IS IMPORTANT
Complete your feedback survey at
http://sim.abel.yorku.ca
https://www.surveymonkey.com/s/LONDONWESTDAYONE
or
For Tomorrow:
Start Time – 8:30 a.m. Breakfast – 7:30 a.m.
Breakout sessions: District teams are asked to send representatives from their team to each of the 4 breakout sessions both in the AM and in the PM sessions. (See summary sheets on your tables for breakout descriptions.)
Feedback Form : Please complete electronic or hard copy feedback form for Day 1
Breakout rooms for Team discussionsDistrict Breakout room for Team discussion
Windsor-Essex CDSB Kensington 1
St. Clair CDSB Kensington 2
Greater Essex County DSB Manchester
Thames Valley DSB London A
London District CSBHuron Perth CDSBAvon Maitland DSBLambton Kent DSBProvincial Schools
Bristol A, B, C
TimeTeam
See you at the Spring 2015 SIM K-12!