Processes Development Department Of Education June 6th, 2008
What are the processes for the Atlantic Provinces Curriculum? The Nova Scotia (Atlantic Provinces) math curriculum has five processes. They are: • Problem Solving • Communication • Reasoning • Connections • Representation
How are the processes stressed? • The Foundation document describes four of the processes in great detail, leaving out representation. • The curriculum documents also only mention four and it is basically a summary of the foundation document. • Foundation document and curriculum guides call them “unifying ideas”, not processes. • All five are mentioned in A Teaching Resource, but with only a brief description of each.
How are the processes embedded? • At least one process is incorporated into every key-stage curriculum outcome as well as every specific curriculum outcome (see report page 2 and 3). • Most KSCOs and SCOs have more than one process included in them. • It is not explicit what processes are included in each SCO. There is a lot of guesswork for teachers. • Problem solving and communication are the most common processes. • Connections is the least common process. They may be implied, but not spelled out in black and white.
How do the documents help teachers use the processes? • In the curriculum documents the worthwhile tasks on the right hand pages often include one or more of the processes (see report page 3 and 4). • In A Teaching Resource, the sample lesson plans ensure teachers are incorporating the processes into their classrooms.
What are the processes for the Quebec Curriculum? The Quebec Education Program (QEP) partitions the mathematical processes into 3 “competencies”: • Solving Situational Problems • Using Mathematical Reasoning • Mathematical Communication
How are the processes stressed? • Quebec’s competencies are the focal point of their document; more developed than any other section. • Elementary breaks the competencies into 3 cycles increasing in difficulty level (see report page 4). • Junior High divides them via 5 topic fields: arithmetic, algebra, probability, statistics, and geometry (see report page 5). • Links each competency to one another as well as success in all other subject fields and the real world. • The “be all end all” of math education.
How are the processes embedded? • The competencies are the central focus of the document. • They are outlined directly and descriptively throughout the document. • Due to the relevance given to them, no embedding occurs. • Charts, images, and descriptive sections within each competency leaves no question as to what is expected.
How do the documents help teachers use the processes? • Elementary stream - gradual increase in difficulty for each cycle allows teachers a how-to guide to instruction (see report page 5). • Secondary stream – each topic field explained through each competency aids teachers instruction. • Easy to read charts, images, and key points guide teachers, showing how the topic should conclude. • Given their relevance, teachers are expected to instruct based on processes versus GCOs and SCOs (is this effective?)
What are the major differences in Quebec and Nova Scotia? • 3 interconnected, closely related competencies (vs 5). • Shifted focus from outcomes and embedded processes, to competencies central to instruction. • Gives what processes link to each topic and how the material should impact the student • Greater detail on each without embedding. • Not divided by grade level, but rather by cycle (Elem) and topic field (Jr High). • Relates processes to all other subjects and real world success.
What are the processes for the Ontario Curriculum? The Ontario curriculum currently lists 7 processes: • Problem Solving • Communicating • Reasoning and Proving • Connecting • Representing • Reflecting • Selecting Tools and Computational Strategies
How are the processes stressed? • The processes are viewed asan essential component of a balanced mathematics program. • The processes are largely interrelated and span over all content. • The curriculum document provides a description of each process that informs teachers of what they are and why they are invaluable to learning mathematics. • Problem solving is being stressed the most. • Aids for teachers, such as the 4 step problem solving model, are being encouraged (see report page 7).
How are the processes embedded? • The processes standards appear embedded in three main areas. • Overall and Specific Expectations(Comparable to Outcomes) – Processes are naturally included in most tasks . • Achievement Charts in Mathematics – Processes are prevalent in assessment categories (see report page 8). • Section ‘Some Considerations for Program Planning in Mathematics’ – Reiterates the importance of incorporating process development.
How do they help teachers think about processes? • Very thorough descriptions at beginning of the document including the importance of process. • When suggesting planning strategies make sure process is present. • Suggested approach to assessment directly incorporates processes.
What are the major differences in Ontario and Nova Scotia? • There are two more: Reflecting and Selecting Tools and Computational Strategies. • more detailed analysis of what each process involves and why teachers should be making efforts to ensure the progression of these processes. • Deep analysis of problem solving: suggested approach of general 4 step method. • Strong ‘visible’ links in suggested assessment tools.
What are the processes for the Alberta Curriculum? There are seven interrelated Mathematical Processes which are: • Communication • Problem Solving • Connections • Reasoning • Mental Mathematics and Estimation • Technology • Visualization
How are the processes stressed? • The 7 processes are expected to be interwoven in both teaching and learning. • The processes are thoroughly explained in the beginning of the Program of Studies. The process which they would like to concentrate on the most would be Problem Solving. • When the document provides the General and Specific Outcomes, in both the subsections Strand and Grade Level, there is a list of the processes involved underneath each Specific Outcome.
How are the processes embedded? • The processes are embedded throughout the document both explicitly and implicitly. • Each Specific Outcome shows the processes which are incorporated. • The Achievement Indicators use appropriate language to show that the processes can be involved in each Specific Outcome. The language is also used throughout the introduction as well as the framework. • The Instructional Focus also discusses the importance of the processes.
How do the documents help teachers use these processes? • Teachers are provided with detailed descriptions of each process. • They are given the related processes for each Specific Outcome. • There are Achievement Indicators which may or may not be used by the teachers, and they would help with assessing the Specific Outcomes and therefore the processes.
What are the major differences in Alberta and Nova Scotia? • The Atlantic Curriculum has five processes while Alberta has seven. • Alberta’s Processes include Mental Mathematics and Estimation along with Technology. • Alberta has a more in-depth explanation of each process. • Alberta provides the processes which are included in each specific outcome.