THE ONTARIO MATHEMATICS PROFICIENCY TEST (MPT)
THE ONTARIOMATHEMATICS PROFICIENCY TEST (MPT)ASSESSMENT BLUEPRINT Education Quality and Accountability Office 2019
ContentsOverview . 4Demonstrating Mathematics Proficiency . 4Underpinning Principles . 4Components of the Mathematics Proficiency Test . 5Big Ideas in Mathematics . 5Assessment Model . 6Number of Items . 6Time Period . 6Framework for Mathematics Content . 7Content Dimensions for Mathematics . 7Subcategories . 7Number Sense . 7Relationships and Proportional Reasoning . 7Measurement (formulas provided) . 7Categories of Knowledge and Skills . 8Financial Literacy . 8Distribution of Assessment Items . 9Distribution of Mathematics Content Dimensions . 9Distribution of the Categories of Knowledge and Skills. 10Distribution of Mathematics Content Dimensions Within the Categories ofKnowledge and Skills. 10Distribution of Mathematics Content Assessment Items . 11Framework for Pedagogy . 12Content Dimensions for Pedagogy . 12Growing Success . 12Learning for All. 12Front Matter of the Mathematics Curriculum . 12Distribution of Assessment Items . 13Distribution of Pedagogy Dimensions . 13Distribution of Pedagogy Assessment Items . 13Page 2 of 27
Assessment Items and Questionnaire . 14Item Types . 14Bias and Sensitivity . 15Non-calculator Items and Calculator-enabled Items . 15Item Bank . 15Item Pre-testing. 16Item Field Testing . 16Questionnaire Items . 16Test Design . 17Test Design Criteria . 17Assessment Delivery Method. 17Construction of Test Forms . 18Mathematics Content Component . 18Pedagogy Component . 21On-demand Test Form Creation . 22Reporting . 22Accommodations and Accessibility . 24Accommodations . 24Accessibility . 24Data Analysis and Security . 25Data Analysis . 25Security . 25References . 26Page 3 of 27
OverviewDemonstrating Mathematics ProficiencyThe Ontario government requires all teacher applicants to demonstrate theirmathematics proficiency through the successful completion of a mathematicsproficiency test. Accordingly, the Ontario Legislature has enacted, as part of the Safeand Supportive Classrooms Act, 2019, amendments to the Ontario College of TeachersAct (OCTA), 1996, that all Ontario applicants (individuals who are enrolled in, or havecompleted, a program of professional education in Ontario) and InternationallyEducated Teacher applicants must successfully complete the MathematicsProficiency Test (MPT) prior to qualification.The principal purpose of the MPT, according to the Ontario Deputy Minister ofEducation, is to “enhance teacher confidence and sense of efficacy in teachingmathematics, which will ensure that students are better prepared for success in allaspects of their lives”.Subsequently, the Ontario Ministry of Education (OMOE) has mandated the EducationQuality and Accountability Office (EQAO) to take responsibility for the development andreporting of the MPT and has issued regulations concerning aspects of the form,content, and operations of the test, details of which are set out in this blueprint.Underpinning PrinciplesThe philosophy of assessment at the Ontario Ministry of Education and at EQAO hasalways been that its primary purpose is to support learning. This philosophy underpinsthe development and operation of the MPT.The MPT is not intended to discourage new teachers from entering the profession nor isit intended to add difficulties to teacher education either for teacher applicants orOntario Faculties of Education (OFOE). Rather, it is, as the Ministry of Education hasmentioned, a means to “enhance teacher confidence” and to support teachers in asubject area where their confidence may be low. Accordingly, the MPT will largely bebased on the principles of Assessment for Learning.The MPT will combine the diagnostic assessment of teacher applicants’ strengths andweaknesses in mathematics content and pedagogy with feedback and opportunities forremediation in those areas shown to be needed. Teacher applicants will have the abilityto reattempt the test to build confidence and confirm their proficiency in mathematics.Page 4 of 27
Components of the Mathematics Proficiency TestThe regulations setting up the MPT call for the test to be composed of two components: A mathematics content component (70% of the test) based on mathematicscontent knowledge from the Ontario Curriculum Mathematics documents (grades3 to 11); and A pedagogy component (30% of the test) based on foundational understandingof the mathematics curriculum, assessment and evaluation practices, as well aslearning for all students centred on Ministry policy documents: Growing Success: Assessment, Evaluation, and Reporting in OntarioSchools - First Edition, Covering Grades 1 to 12, 2010 (Growing Success), Learning for All: A Guide to Effective Assessment and Instruction for AllStudents, Kindergarten to Grade 12, 2013 (Learning for All), and the Front matter of the Ontario Curriculum mathematics documents1. Thisrefers to the pages of each curriculum document that precede thecurriculum expectations for the specified grades (Front Matter).Big Ideas in MathematicsThe MPT is not intended to assess all the mathematics skills and knowledge fromGrades 3 through 11. The assessment items that comprise the mathematics contentcomponent of the MPT will be based on core understandings, otherwise known as bigideas, surrounding important content dimensions in mathematics. Big ideas inmathematics involve the interconnectedness of concepts “that form a framework forlearning mathematics in a coherent way”.2The MPT is developed on the principle that it is critical for teachers to have a goodgrasp of how mathematical concepts are inter-connected through overarching big ideas.“Teachers need to understand the big ideas of mathematics and be able to representmathematics as a coherent and connected enterprise.” (Martin & Herrera, 2010, p.16).The blueprint for the MPT involves overarching big ideas based on the followingimportant mathematics content dimensions, as reflected in the Ontario curriculum: Number Sense, Relationships and Proportional Reasoning, and Measurement.Assessment items will be embedded in contexts that reflect big ideas of the above threemathematics content dimensions so teacher applicants can demonstrate proficiency inkey principles of mathematics knowledge and will apply mathematical reasoning.31Ontario Ministry of Education. (2005a). The Ontario curriculum, Grades 1-8: Mathematics.Ontario Ministry of Education. (2005b). The Ontario curriculum, Grades 9-10: Mathematics.Ontario Ministry of Education. (2007). The Ontario curriculum, Grades 11-12: Mathematics.2Ontario Ministry of Education, 2005a, p.43Ontario Ministry of Education, 2005b, 2007Page 5 of 27
Assessment ModelTeacher applicants will attempt the MPT in a proctored environment using a computerbased testing (CBT) delivery method. They will have the ability to select a test session4(during a test window) on the platform according to their choice based on timing,location, available test sessions, and required accommodations.The MPT will be automatically machine-scored and will provide diagnostic feedback onthe performance to the teacher applicants within 10 days5 of completion of the test. Thefeedback will provide teacher applicants with their overall performance on both themathematics content and pedagogy components of the test along with whether theywere successful in each component. Additionally, they will receive feedback on themathematics content dimensions and the associated categories of knowledge and skills,to support in identifying areas of the assessment they hold a strong understanding andareas of the assessment they need to remediate.Upon completion of the assessment and receiving feedback, teacher applicants willhave the opportunity to upgrade their skills. They can reattempt the MPT as many timesas they would like, or as needed, based on the test session availability.Number of ItemsThe MPT will have 75 items. Each unique test (test form) will contain 71 items thatcount towards the teacher applicant’s score. These will be 50 mathematics contentitems (70% of the test) and 21 pedagogy items (30% of the test).The first 5 mathematics content items will cover the knowledge and understanding ofnumber sense. Teacher applicants will be required to solve these items without the useof a calculator. The remaining 45 mathematics content items can be answered with theuse (if desired) of a built-in calculator on the platform. The mathematics content itemswill be drawn from a test bank of over 250 psychometrically validated assessmentitems. The pedagogy items will be drawn from a test bank of over 100 items.In every test administration, 4 field test items (that will not count towards the teacherapplicant’s score) will be included. These will be 1 non-calculator item, 2 calculatorenabled items, and 1 pedagogy item.Time PeriodThe MPT is designed to be completed in a 2-hour time period.6 This will provideteacher applicants with a little over 1 ½ minutes per item, although, some items couldtake teacher applicants a few seconds to attempt, resulting in more time allocated towhat teacher applicants would perceive as more complex problems.4Test sessions are time periods that are pre-set by test administrators (OFOE) for teacher applicants toattempt the MPT. Test windows are time periods that are pre-set by EQAO for test administrators tocreate test sessions. EQAO has planned to have four, month-long test windows every year: winter,spring, summer, and fall.5The results are immediately made available for EQAO to review and validate prior to the report beingautomatically emailed from the system to the respective candidate.6Additional accommodations can be provided if required. See Accommodations and Accessibility section.Page 6 of 27
Framework for Mathematics ContentContent Dimensions for MathematicsThe mathematics content component of the MPT is designed to assess theunderstanding of big ideas based on the three mathematics content dimensions thatencompass a wide range of learning expectations from Grade 3 to Grade 11 within theOntario Mathematics Curricula. The mathematics content dimensions are: numbersense, relationships and proportional reasoning, and measurement.The content of the assessment items are embedded in contexts that reflect big ideas inmathematics. This will enable teacher applicants to demonstrate their understanding ofkey fundamental principles in mathematics and the application of mathematicalreasoning. (OMOE, 2005b, p.23)SubcategoriesThe subcategories of the mathematics content dimensions are interrelated andrepresent fundamental mathematics concepts. The assessment items in the MPT coverall the subcategories to ensure that a balance of concepts is assessed. The blueprint forthe mathematics content component of the MPT includes the following subcategories:Number Sense Operating with whole numbers, integers, decimals, and fractions: addition, subtraction,multiplication, division, and square root Expressing whole numbers using place value and expanded form Working with exponents Evaluating numeric expressions involving order of operationsRelationships and Proportional Reasoning Ordering and comparing whole numbers, integers, decimals and fractionsUsing relationships among fractions, decimals, and percentWorking with percentWorking with ratios, proportions, rates, and unit ratesSolving problems involving proportional thinkingSolving problems involving probabilityRecognizing linear vs non-linear relationshipsRepresenting linear relations: graphically, numerically, and algebraicallySolving first degree equationsSolving linear systems graphicallySolving mean, median, and modeMeasurement (formulas provided) Applying Pythagorean theoremSolving problems involving conversions of metric units (perimeter, area, and volume).Solving problems involving perimeter of regular and irregular shapes and circlesSolving problems involving area of regular and irregular shapes and circlesSolving problems involving surface area of prisms and cylindersSolving problems involving volume of prisms and cylindersPage 7 of 27
Categories of Knowledge and SkillsThe mathematics content assessment items are categorized under one of the threecategories of knowledge and skills: Knowledge and Understanding: assesses the basic knowledge andunderstanding of mathematics concepts.For example, demonstrating an understanding of the tenths place value indecimal numbers. Application: assesses the use of knowledge and understanding to makeconnections within and between various contexts. (OMOE, 2005a).For example, applying the relationship between area and perimeter to solve forthe area of a shape. Thinking: assesses critical thinking processes.For example, the use of critical thinking to find the surface area of two attachedcubes.A higher proportion of assessment items are mapped to the Application category ofknowledge and skills since the MPT is a minimum-competency mathematicsassessment and teacher applicants will need to demonstrate that they can apply theirknowledge and understanding of mathematics concepts to various contexts using avariety of tools and strategies to solve problems.Financial LiteracyThrough mathematics concepts, financial literacy engages major themes such aspersonal finances, budgeting, consumer literacy, and economic contexts (OMOE,2016a; OMOE, 2016b). At least 12 mathematics content items (24% ) of themathematics content component of the MPT will have a financial literacy context. Theseitems will cover content from any of the mathematics content dimensions and any of thecategories of knowledge and skills.Money amounts and financial literacy are embedded in specific mathematical learningexpectations seen throughout The Ontario Mathematics Curricula. We can see this inGrade 3 Number Sense and Numeration where students are expected to “represent(using the symbol) the value of a collection of coins” (OMOE, 2005a, p.55), all the wayto Grade 11 where “Students will solve problems associated with earning money,paying taxes, and making purchases; apply calculations of simple and compoundinterest in saving, investing, and borrowing; and calculate the costs of transportationand travel in a variety of situations” (OMOE, 2007, p.77).Financial literacy is not only important when it comes to the Ontario Curriculumexpectations but is embedded in the daily lives of people. The MPT will cover financialliteracy in day-to-day contexts, such as earning and purchasing; saving, investing, andborrowing; and scenarios related to transportation and travel.Page 8 of 27
Distribution of Assessment ItemsThis section describes the distribution of the mathematics content dimensions andcategories of knowledge and skills that make up the mathematics content component(70% of the MPT) of test forms.Distribution of Mathematics Content DimensionsThe MPT is designed to assess the Knowledge and Understanding, Application, andThinking strategies of big ideas in mathematics based on the following mathematicscontent dimensions: number sense, relationships and proportional reasoning, andmeasurement.The Ontario Curriculum, Grades 1-8: Mathematics states, under the strand NumberSense and Numeration, that “a well-developed understanding of number includes agrasp of more-or-less relationships, part-whole relationships, measures in theenvironment, and much more” (OMOE, 2005, p.8). It also states that represen
The Ontario curriculum, Grades 11-12: Mathematics. 2 Ontario Ministry of Education, 2005a, p.4 3 Ontario Ministry of Education, 2005b, 2007 . Page 6 of 27 Assessment Model Teacher applicants will attempt the MPT in a proctored environm
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