1997 Provincial Learning Assessment in Mathematics

Summary of Grade 8 Findings  For Teachers at the Middle Level

This learning assessment used paper-and-pencil and performance station tests to collect data on mastery and application of mathematics concepts by Saskatchewan students in Grades 5, 8, and 11. A similar assessment was conducted in 1995.   The Provincial Learning Assessments are part of the Saskatchewan Indicators Program. The Saskatchewan Curriculum Evaluation Program and other national and international assessments and surveys are also components of the Indicators Program. The findings from these sources help guide educational practice in Saskatchewan.

Opportunity Results
Do Saskatchewan Grade 8 students have adequate opportunities to learn mathematics?
Students, parents, and educators share responsibilities for students’ learning mathematics. A panel of education partners including teachers and trustees met to set provincial expectations for eight elements indicating Saskatchewan students’ opportunities to learn mathematics. These expectations and related findings are shown in the following figure.
		One-quarter of Grade 8 students use manipulatives at least 7 times per month (1.8 times/wk) to concretely represent math concepts and solve math problems. More than one-half never have this opportunity. Fewer than 30% of Grade 8 students report learning mathematics in small-group settings as frequently as the 2.6 times/week provincial standard. About one-quarter of Grade 8 students report never having opportunity to learn mathematics in small-group settings. The potential of the computer and the Internet is not being realized in the mathematics classrooms of Saskatchewan. Two-thirds of Grade 8 students persist to do their best when solving math questions. About one-third spend time doing mathematics homework as frequently as expected. Only 11% set goals prior to class and 44% commit to paying attention to class activities. The percentage of parents providing sufficient support is near expectation.

Outcome Results
Numbers of Grade 8 students attaining good and top level problem-solving achievement were below provincial expectations. Fewer than expected could adequately communicate their understanding and strategies ...
How well do Grade 8 students solve problems? Grade 8 students’ achievement in solving problems was below expectations. In the performance station test, 54% of the students showed good achievement (Level 3 or above). Sixty-nine percent were expected to do so. Fewer than expected attained top level achievement. While 7% were expected to attain Level 5, only 2% did so.	Students solved problems presented at performance stations. Student achievement was judged holistically, one level assigned to the student's entire work. · Level 5 is the best work of our most capable students. · Level 4 indicates high proficiency and application skills. · Level 3 is sound, adequate, and consistent work. · Level 2 lacks consistency, showing only basic understanding of routine mathematics. · Level 1 is limited and poor performance.
How well do Grade 8 students communicate their strategies and mathematics understanding? The work of 33% of Grade 8 students was judged to be Adequate Communication when detailing their work, describing their strategies, and explaining their reasoning. A further 10% of Grade 8 students showed Proficient Communication in their work. These were below the expectations that 47% would show Adequate Communication and 14% would show Proficient Communication.  What are Grade 8 students’ attitudes toward mathematics? Nine of ten Grade 8 students believe the mathematics they learn is useful. About 70% think it will help with future schooling and 60% use their mathematics in everyday life. About 56% of Grade 8 students like mathematics and nearly 70% are confident when they solve math problems.	Three categories were used to describe students' written communication in mathematics: · Proficient Communication work contains elements of precision, clarity, and elaboration explanations contain math terminology and are supported by diagrams, graphs, or examples · Adequate Communication explanations lack detail and use common language solutions are sufficiently clear · Beginning Communication limited work shown explanations or work provided are difficult to follow
	For Grade 8 males, there was a significant relationship between achievement and attitudes. Boys who like math scored significantly higher than boys who don't like math. This was not evident for Grade 8 females. At this grade, the assessment found girls who like math performed similarly to girls who don't like math.

Suggestions For ...
Making Problem-Solving the Activity for Exploring and Learning Mathematics in the Classroom Use a variety of problem types (translation, process, and realistic) as described on page 609 of the curriculum guide. Use daily problem-solving activities and "Feature Problems" to develop students’ creative and critical thinking. Encourage them to use and discuss a variety of strategies for solving problems. Some of these are outlined on page 806 of the curriculum guide. On pages 1053-1082 of the curriculum guide, a sports-related model unit contains several problem-solving activities for the Grade 8 classroom.	Where can you find problems? · Page 609 and 805 of the curriculum suggest possible sources for teachers and students to find or create problems. · If you have access to the Internet, you may wish to check out these problem-solving site addresses: http://mathforum.org/dr.math/drmath.middle.html http://mathforum.org
Actively Involving Students in Exploring and Learning Mathematics Allow students choice when selecting, creating, and solving problems. For example, students might design and conduct their own data management projects. Give opportunities for students to use fraction blocks and/or strips, integer tiles, algebra tiles, and other materials to build a good understanding of math concepts. Such understanding contributes to efficient and proper application of algorithms. Use structured activities and discussion to transfer this understanding to abstract representations and new situations. Provide opportunities for students to work on math projects and solve problems cooperatively. Use quality software and Internet sources that allow students to explore various math topics.   Increasing Students’ Communication of Their Mathematics Understanding Structure group-work activities where students discuss and compare their strategies as they solve problems. Use cooperative learning and other techniques to assign students various roles as they work together. Expect students to show and/or explain their solutions. Encourage students to reflect on their understanding and solutions. Journals may be useful for this. For example, having students construct concept webs for the rational number system develops their understanding and communicates it to the reader.	Sources and Ideas · Check out the section "Steps to Teaching Problem-Solving: An Example" on pages 47-49 of the curriculum guide. · Suggestions for the types and uses of manipulatives are found throughout the curriculum guide. · Manipulatives can be home-made. A selection can be purchased from the Saskatchewan Learning Resources Distribution Centre. · The 6th Edition of Ideas & Resources for Teachers of Mathematics (November 1997) contains several ideas for actively involving students in learning geometry concepts. This is a publication of the Saskatchewan Mathematics Teachers' Society. · SIDRU and SPDU publication lists include 18 quality booklets in their Instructional Strategies Series. Opening the Door to Cooperative Learning is one in this series. These booklets are available from the Saskatchewan Learning Resources Distribution Centre. · NCTM magazines, Teaching Mathematics in the Middle School · Other math resource and discussion websites: http://www.sasked.gov.sk.ca/curr_inst/scitech http://MathCentral.uregina.ca/ http://www.nctm.org http://otresources.ti.com/ http://mathforum.org/ http://mathforum.org/~steve/steve/mathmid.html http://www.mste.uiuc.edu/