1997 Provincial Learning
Assessment in Mathematics

 

Summary of
Grade 5
Findings

 

For Teachers
at the
Elementary
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 5 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.

  • About one-third of Grade 5 students use manipulatives at least two times per week to concretely represent math concepts and solve math problems. Almost one-third never have this opportunity.

  • Most Grade 5 Saskatchewan students do not work in groups as frequently as expected. Almost 15% report never having opportunity to share ideas and explore problems through group activities.

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

  • About two-thirds of Grade 5 students persist to do their best when solving math questions and spend time doing mathematics homework as frequently as expected. Fewer set goals and commit to paying attention to class activities.

  • The percentage of parents providing sufficient support is near expectation.

 

OUTCOME RESULTS

A challenge exists to increase Grade 5 students' mastery and application of math concepts to meet standards for good and top level math achievement ...

How well do Grade 5 students solve problems?

  • Grade 5 students' achievement in solving problems was close to expectations. In the performance station test, about 54% of the students showed good achievement (Level 3 or above). About 58% did so in the paper-and-pencil problem-solving test.

  • Fewer than expected attained top level achievement. While 7% were expected to attain Level 5, about 3% did so on the performance and paper-and-pencil tests.

Students solved problems presented:

  • at performance stations

  • on a paper-and-pencil test

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 one-half of Grade 5 students showed either Adequate Communication (43%) or Proficient Communication (7%) when showing their work, describing their strategies, and explaining their reasoning.

  • This was below the expectations that 51% would show Adequate Communication and 18% would show Proficient Communication.

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

How well do Grade 5 students perform
calculations and apply content?

  • Grade 5 students correctly answered 63% of questions involving addition, subtraction, multiplication, and division calculations with whole numbers and decimal numbers.

  • In a 40-item multiple-choice test assessing students' mastery and application of content, the average score was 52%. Lowest performances occurred in the Fractions and Decimals and in the Geometry strands. Students scored best in the Data Management strand.

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 pages 508-509 of the curriculum guide.

  • Encourage students to use and discuss a variety of strategies for solving problems. These are outlined on pages 506-508 of the curriculum guide.

  • Develop students' creative and critical thinking through daily problem-solving and interesting and challenging "Feature Problems of the Week".

 

Where can you find problems?

Actively Involving Students in Exploring and Learning Mathematics

  • Allow students choice when selecting, creating, and solving problems. For example, the curriculum (pp. 514-519) suggests options for student decision-making when collecting, organizing, and analyzing data.

  • Listen to students' theories as they use manipulative and/or represent strategies to model math concepts and test problem-solving. This is particularly useful when studying fractions and geometry concepts. Use structured activities and discussion to transfer 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 techniques to assign students various roles as they work together.

  • Expect students to show and/or explain their solutions.

  • Pages 510-513 of the curriculum describe activities as students reflect on their understanding and solutions. Writing journals may be useful to reflect on and further explore math concepts. For example, having students "Tell (or show) you everything they know about one-quarter" can both allow them to construct understanding and communicate this to the reader.

 

 

Sources and Ideas

  • 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 and 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 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 Children Mathematics

  • Other math resource and discussion websites:

    http://www.sasked.gov.sk.ca/curr_inst/scitech
    http://mathcentral.uregina.ca/
    http://www.nctm.org
    http://mathforum.org/
    http://math.rice.edu/~lanius/Patterns/
    http://www.mste.uiuc.edu/