Mathematics

Technologies must be seen as important problem-solving tools. Computers and calculatorsare tools of mathematicians, and students should be given opportunities to select anduse the learning tools that may be helpful to them as they search for their own solutionsto problems.It is important that teachers introduce the use of technology in ways that build students’confidence and contribute to their understanding of the concepts being investigated,especially when students may not be familiar with the use of some of the technologiessuggested in the curriculum. Students’ use of technology should not be laborious orrestricted to inputting and learning algorithmic steps. For example, when using spreadsheetsand statistical software (e.g., Fathom), teachers could supply students with prepareddata sets, and when using dynamic geometry software (e.g., The Geometer’s Sketchpad),pre-made sketches could be used to ensure that students focus on the important mathematicalrelationships, and not just on the inputting of data or on the construction of thesketch.Whenever appropriate, students should be encouraged to select and use the communicationstechnology that would best support and communicate their learning. Computersoftware programs can help students collect, organize, and sort the data they gather, andwrite, edit, and present reports on their findings. Students, working individually or ingroups, can use Internet websites to gain access to Statistics Canada, mathematics organizations,and other valuable sources of mathematical information around the world.ManipulativesAlthough technologies are the most common learning tools used by students studyingsenior level mathematics, students should still be encouraged, when appropriate, to selectand use concrete learning tools to make models of mathematical ideas. Students need tounderstand that making their own models is a powerful means of building understandingand explaining their thinking to others.THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics20Representation of mathematical ideas using manipulatives 4 helps students to:see patterns and relationships;make connections between the concrete and the abstract;test, revise, and confirm their reasoning;remember how they solved a problem;communicate their reasoning to others.Computational StrategiesProblem solving often requires students to select an appropriate computational strategysuch as applying a standard algorithm, using technology, or applying strategies related tomental computation and estimation. Developing the ability to perform mental computationand to estimate is an important aspect of student learning in mathematics. Knowingwhen to apply such skills is equally important.4. See the Instructional Approaches section, on page 30 of this document, for additional information about the use ofmanipulatives in mathematics instruction.