Overview                              .Introduction                                                   Teaching and Reporting on the Five Strands                           Assessment in Mathematics

Homework                                   Teaching in the Combined Class

Specific activity suggestions

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Implementation Guidelines for Student and Program Assessment

Metropolitan Separate School Board, 1997.

The main purpose for the assessment and evaluation of children is to improve learning and to ensure effective programming. As stated in the Implementation Guidelines for Student and Program Assessment, effective assessment practices must be:

Traditional mathematics programs focussed instruction on one topic or area of mathematics at a time, with an emphasis on the mastery of traditional paper and pencil algorithms and formulas. Today the vision of mathematics calls for reasoning, problem solving, communication, and making connections across the strands of mathematics and with other areas of the curriculum. Teachers are encouraged to engage students in "rich learning tasks" that often integrate the strands. The assessment of these tasks should reflect their multi-stranded approach.

A complete mathematics program includes open-ended investigations, co-operative group experiences and thought provoking activities all designed to provide students with meaningful experiences that will develop their problem solving and communication skills. What we assess, communicates to students what we think is important.

The Ontario Curriculum, Mathematics (1997) states

"A student will be assessed on how well he or she solves problems, shows understanding of concepts, applies mathematical procedures, and communication of knowledge. For each of these categories there are four levels of achievement."

A chart describing student performance for each of the four knowledge and skills categories can be found on page 9 of The Ontario Curriculum Grades 1-8. These categories help teachers assess how well a student has met the expectations. Teachers need to continue to develop strategies for assessing how well a student solves problems, shows understanding of concepts, applies mathematical procedures, and communicates required knowledge. Some suggestions are listed below:

Adapted from "Getting Assessment Right: Mathematics" by Damien Cooper, Nanci-Wakeman-Jones, Pat Blake, Data Based Directions

Assessing students under the four knowledge and skills categories requires strategies that go beyond using the traditional paper and pencil test or quiz. It has been said that using one assessment for a wide range of purposes is like using a hammer for a wide range of jobs from pile driving to brain surgery. Additional assessment tools, such as the ones described in the chart above, are needed. The text programs currently available offer extensive support for teachers by providing a positive and balanced assessment plan. Look for references to assessment tools that include:

In addition to ensuring students have the opportunities to meet expectations addressed by all four knowledge and skills categories, teachers need to develop an understanding of what student performance looks like at all four levels of achievement. Consistency will be achieved when teachers develop a common understanding of what student work looks like at all four levels of achievement, given any grade or category . To help support teachers in this process the Ministry of Education has released mathematics exemplars which provide samples of student work to review and discuss with colleagues. Teachers are also encouraged to collect samples of student work at each of the four levels of performance and use them as examples for students to see. Parents will also find examining samples of student work helpful.

As we continue to implement the new curriculum, we will work towards ensuring that the three circles above eventually align into one. When this happens, the curriculum delivered in the classroom, along with the curriculum that is being assessed with be based on the curriculum expectations in the Ontario Mathematics Curriculum.

Additional information on assessment can be found in Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions (NCTM, 1991). This document (yellow cover) was provided to all schools in 1995.

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Reporting On The Five Strands

The Ministry of Education and Training requires teachers to report on student achievement in each of the five strands in mathematics. In the past, teachers were required to report on three strands in the first term and all five strands in the second and third terms. The policy for reporting on the five strands was amended on September 1, 2000. The new policy is as follows and replaces the policy stated in the Guide to the Provincial Report Card, Grades 1-8, 1998.

First, Second, and Third Reporting Periods. Fill in the student’s grade/mark for each strand that is part of the student’s instructional program. If a particular strand is not part of the student’s program during a reporting period, indicate this in the comments and leave the grade/mark column blank.

A grade/mark must be filled in for each strand at least two reporting periods, and each reporting period must show a grade/mark for at least two strands.

This planning guide has been organized to reflect the change in policy. In the overview, each strand has been addressed in two of the three reporting periods. The suggested strands for each reporting period have been identified in the scope and sequence chart. It is important to note that reporting on student achievement, for all subject areas, is not cumulative from one term to another. It is to reflect what the student has achieved during each specific term.

Strand Treatment in Current Text Programs

Current text programs tend to address more than one strand in a unit, although the name of the unit may suggest otherwise. For example, in the Quest 2000, grade 6, unit 1 "Exploring Relationships and Graphs", while the major focus is on Data Management and Patterning and Algebra, all of the other strands are addressed in varying degrees.

To assist teachers in identifying the strands addressed in each unit, this curriculum planning guides correlates each unit to the mathematics expectations from the Ontario Curriculum. Each unit overview lists the expectations being addressed. The scope and sequence chart is designed to assist teachers with planning assessment and evaluation for their program. Local needs may require teachers to make some adjustments.

Preparing for the EQAO Provincial Assessment in Mathematics

The best way to prepare students for the Grade 3, 6 and 9 EQAO assessments in mathematics is to ensure that students have the opportunity to meet the expectations in the rich ways described in the curriculum. Students need to be actively involved in exploring, investigating, problem-solving, reasoning, justifying, manipulating, applying and communicating. This, by no means, is a one year job. Students need to develop these skills throughout the Primary, Junior and Intermediate programs. Although sample assessment tasks are available, simply exposing students to these "practice" opportunities is not enough. Embedding investigations, and problems, such as those administered by EQAO, into the regular mathematics program, will best prepare our students for these assessments.

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All learning activities must be carefully selected to help students meet the broad range of expectations listed in the Ontario Curriculum for Mathematics. This also applies to homework. The teacher must ensure that the homework program offers a variety of activities that meet the specific needs of all students in the class. Homework assignments should be manageable for both child and parent. Although the amount of homework will vary, it should be included regularly.

Homework should take on a variety of forms that include:

Careful consideration must be given to the amount and type of homework assigned. Monitor how long students are spending on their mathematics homework. Get feedback from both students and parents. If a student seems to be struggling with homework, it may be appropriate to modify the workload.

Some parents have expressed concern over not being able to help their children with an investigation or activity because they are not familiar with the expectations being addressed. Be careful not to send home activities designed as a group investigation or requiring significant teacher direction. Research tells us that parents are very comfortable with helping their children develop proficiency with the traditional skills. Ensure that the homework provides ample opportunity for parents to support your program in this way.

The Role Of Workbooks

Please note that there are several publishers who are marketing homework books. They include "Quest 2000: Homework and Practice" by Addison Wesley Longman, "Connections In Math" by Guerin and "My Ontario Math Workbook" by Irwin. You may wish to recommend these workbooks to parents who wish to supplement the mathematics program with extra practice for their children. These workbooks focus primarily on helping students consolidate skills. Some teachers have considered using these wrokbooks as part of their program. Teachers must always guard against reducing their mathematics program to a series of drill and practice exercises that primarily engage students in the rote memorization of procedures and may rob them of the time to experience rich opportunities to develop a solid understanding of the key concepts.

Teaching the current math program in a combined grade situation is quite a challenge and there is no perfect answer to the problem of how best to handle it. This challenge arises from the fact that an effective mathematics program requires students to work in cooperative groups, use manipulative materials, solve problems, and communicate.

The publishing companies and teachers have developed strategies for teaching in a combined classroom. The following are some suggestions you may wish to consider. A combination of these suggested strategies is recommended based on the individual and whole group needs of your class.

Teaching the Grades Together Where Topics Match

	Identify topics/Ontario Curriculum expectations that match
	Use the lower grade Teacher’s Guide and provide extensions and additional challenges for the higher grades or use the higher grade Teacher’s Guide and make modifications for the lower grade (choice of Teacher’s Guide will depend on make-up of class)
	Instruct the group separately for topics/Ontario Curriculum expectations that do not match.
	Communicate with other teachers to avoid duplication of units across the years.
	Note: Schools will be provided with "Mathematics Expectations Continuum: Grades K-8 which help them to identify where topics overlap

 

Teaching the Grades Together by Combining the Teacher’s Guides

	Select some units from each grade level
	Instruct the class as a whole using a combination of these units
	Make modifications where necessary to accommodate each grade level
	Communicate with other teachers to avoid duplication of units across the years
	Teachers need to be careful that all the expectations for each grade level have been addressed

 

Teaching the Grades in Isolation

	Instruct each grade separately
	While one group is receiving instruction, the other group engages in another math activity (e.g., exploration centres, continuation of previous day’s Core Activity, suggested "Extensions" or "Additional Lessons" from previous day’s Core Activity, a skills consolidation exercise, problem solving activity, previously-learned games, "Math Journal" or "Word Glossary" writing)
	In some classrooms, while one grade is working on mathematics, another may be engaged in work from a different subject area

 

 

 

Teaching the Grades Separately but Coordinating the Topics

	Instruct each group separately but coordinate the topics/Ontario Curriculum expectations for the two grades wherever possible so that the whole class is working on a common theme
	Students may be able to work together on some activities

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