1997 Provincial Learning
Assessment in Mathematics

 

Summary of
Grade 11
Findings

 

For Teachers
at the
Secondary
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 11 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 11 students use manipulatives at least once per week to concretely represent math concepts and solve math problems.

  • About 36% of Grade 11 students report learning mathematics in small-group settings at least twice per week. Thirty-seven percent of Grade 11 students report never having this opportunity.

  • The potential of the computer and the Internet is not being realized in the mathematics classrooms of Saskatchewan.

  • Over 60% of Grade 11 students persist to do their best when solving math questions. Fewer than 25% spend the expected 2.6 hours per week doing mathematics homework. Only one in ten sets goals prior to class. About one-half of Grade 11 students commit to paying attention in class activities.

  • Parents of Grade 11 students exceed expectations for discussing academic progress and helping with assignments. Fewer than expected attend school interviews.

 

OUTCOME RESULTS

Insufficient numbers of Grade 11 students attained good problem-solving achievement. Fewer than expected could adequately communicate their understanding and strategies...

How well do Grade 11 students solve problems?

  • Grade 11 students' achievement in solving problems was below expectations. About two-thirds of the students showed good achievement (Level 3 or above). Seventy-nine percent were expected to do so.

  • Numbers achieving top level performance were near expectations. While 11% were expected to attain Level 5, about 8% 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 5 students communicate their strategies and mathematics understanding?

  • About 63% of Grade 11 students showed Adequate Communication (42%) or Proficient Communication (21%) when detailing their work, describing their strategies, and explaining their reasoning.

  • The 21% showing Proficient Communication met the expectation that 18% would do so. However, the expectation that 69% would show at least Adequate Communication was not met.

Three categories were used to describe student's 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

What are Grade 11 students' attitudes toward mathematics?

  • Over 80% of Grade 11 students believe the mathematics they learn is useful. About 70% think it will help with future schooling. Fewer than one-half use the concept or processes learned in their math classroom for everyday life.

  • About 57% of Grade 11 students like mathematics and 55% are confident when they solve math problems.

Grade 11 males and females achieved similar overall results. Females communicated their math understanding and strategies more proficiently than males.

Grade 11 students who like math and/or have confidence in their math abilities attained higher achievement than those who don't.

SUGGESTIONS FOR ...

Developing Creative and Critical Thinking Through Problem Solving

  • Give students a variety of problem types (translation, process, and realistic). Encourage them to use and discuss different strategies.

  • Use regular problem-solving activities to develop these strategies and skills. Extend the problems to recognize patterns, justify findings, further explore applications, and develop persistence.

Actively Involving Students in Exploring and Learning Mathematics

  • Consider "consumer mathematics projects" which integrate math skills with social issues and decision-making. Students might mimic or create family or business financial situations. Where possible, allow students choice when selecting, creating, and solving problems.

  • Use technology including graphing calculators, quality computer software, and the Internet to explore mathematics concepts and relationships. These are particularly useful when investigating functions and equations, probability, and geometry.

  • Allow for multiple representations of problems. Assist students who benefit from the concrete representation provided by manipulatives such as algebra tiles, mira, and fraction blocks and/or strips. Guide students in their use and relate it to more abstract representations and new situations.

  • Provide opportunities for students to work on math projects and solve problems cooperatively.

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, peer tutoring, 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, students might describe, explain, and contrast real-world situations depicted by graphs. This can both develop students' understanding of key features of quadratic functions and communicate it to the reader.
     

 
Sources and Ideas