1 ELL Regional STEP Session ELL Initial Mathematics Assessment Materials Needed:Per participant:A copy of the assessment flow chartA copy of the information about the assessment (overall messages/guidelines)Per table:Sufficient copies (for sharing) of the grade two student booklet, teacher/assessor booklet, and checklist/observation form based on one copy for every two participantsSufficient copies (for sharing) of the grade seven assessment student booklet, teacher/assessor booklet, and checklist/observation form based on one copy for every two participantsIf possible, base ten blocks11
2 Every day, more than one million English language learners attend Ontario’s publicly funded schools. They come from every country and every circumstance. They bring with them a valuable world perspective needed by all students to operate successfully in a global community.Supporting English Language Learners: A practical guide for Ontario educators, Grades 1 to 8, 2008, p. 17
3 AgendaFocused Conversations about the ELL Math Assessment Tool including:Background information and overviewMaterials and organizationGuidelines for implementationMathematical knowledge/concepts2
4 Our Shared GoalsIt is important that newly arrived English language learners receive a warm welcome during their transition into our Ontario schools. The initial assessment process has a strong impact on the first impressions of these students and their families. During this process, it is critical that educational staff take the opportunity to learn about the whole child and celebrate the diversity each student will bring to our classrooms.
5 Using the Initial Mathematics Assessment Tool for English Language Learners, Grades K – 8 This tool is not intended to be a replacement for the ongoing assessment gathered by the classroom teacher. It is through a variety of assessment strategies and tools that the programming needs of all students are best addressed.Have participants read the bullets found under the quote in the Rationale and Assessor Instructions document provided for each participant.
6 Guidelines for Initial Assessment Development Begin with counting and simple computation.Give students access to manipulatives and geometric shapes.Encourage students to skip over items that seem unfamiliar and look for others that they understand.Assess a student’s knowledge of key concepts and skills in all five strands of the Ontario mathematics curriculum appropriate for the grade level (e.g., if an English language learner is placed age-appropriately in Grade 5 in September, then assess knowledge of the Grade 4 mathematics curriculum. If the student arrives in January, assess some of the mathematical concepts already covered in Grade 5 as well.)Accept different ways to show calculations, as long as they yield correct answers.Supporting English Language Learners: A practical guide for Ontario educators, Grades 1 to 8, 2008, pProvide some background as to the development/field testing process:Writing began in summer of Strand assessments created (all five strands) for grades k-8Field testing was conducted in the spring of 2010 (5 boards in Ontario)Revisions were done in summer of 2010 (based on feedback from the field testers)Now…provincial launch…
7 Materials Assessment Flow Chart Grade level packages which include: One assessment tool for each mathematical strandTeacher Instruction and Observation Page by strand (including materials) and Student Booklet (for Number Sense and Numeration grades 1-8 only)List of process expectations relating to the Number Sense and Numeration problem solving question included in the grade 1 to grade 8 assessmentsList of expectations addressed in each strand assessment toolNote that for the NS and N strand only…there is the other available checklist/observation sheet
8 Begin with the Flowchart Participants should have individual copies to refer to as discussed. Review key points.
9 Initial Mathematics Assessment Tool for English Language Learners, Grades K – 8 Aligned with Ontario Mathematics curriculum expectationsGrade specific assessment tools are based on previous grade curriculum expectationsStudent assessments do not show specific grade level but are coded by letter:A (kindergarten/grade one assessment based on kindergarten expectations)B (grade two assessment based on grade one expectations)C (grade three assessment based on grade two expectations)D (grade four assessment based on grade three expectations)E (grade five assessment based on grade four expectations)F (grade six assessment based on grade five expectations)G (grade seven assessment based on grade six expectations)H (grade eight assessment based on grade seven expectations)
10 Using the Initial Mathematics Assessment Tool for English Language Learners, Grades K – 8 For each grade level strand assessment, a cluster of expectations has been selected to provide a starting point in determining the mathematical knowledge and skills of the student. It would not be reasonable or appropriate to assess all curriculum expectations within this initial assessment.
11 Taking a Closer Look at the Features of the Number Sense and Numeration Assessments Teacher/Assessor CopyStudent CopyUsing grade two as an example (all five strands), discuss text features, including:The teacher and student booklet are only separate in the NS and N strand – in all other strands there is only one booklet (teacher/assessor). The exception to mention is grade 1 (there is only a teacher/assessor booklet)Note***There is a choice of two different note taking sheets for the teacher/assessor (note the checklist vs the anecdotal recording sheet)Look at checklist first:Note information box at bottom For the AssessorNote the box at bottom MaterialsNote the student information section at the top of the pageNote curriculum alignment – overall expectations and specific knowledge and skillsLook at second version (anecdotal version of teacher/assessor booklet)Note Materials and/or visual aids neededNote section Notes to TeacherNote student information sectionNote boxes for anecdotal notes/observationsLook at first question (Read and Write Whole Numbers to 50)…What are some observations/assessment notes that could be noted? Discuss whole group. Note that this question does appear in all the preceding grades. This was done to allow an access point for students – even when grade level curriculum deals with higher numbers, it is still dependant on students being able to read and write numbers to 100.Compare student book with teacher/assessor booklet. Note that there are usually additional questions available on the teacher/assessor copy. These questions will use manipulatives/visual aids and will have limited and/or no recording on paper.Look at alternative observation/checklist formNote the information sections regarding materials and/or visual aids and notes to teacherNote the student information section at top of sheetNote how the questions have been clustered around the overall expectations
12 Important Considerations ELLs arrive in our Ontario schools with varying background experiences and English language acquisition skills. The teacher/assessor should always consider the individual student needs, and use professional judgement in the use of this assessment tool. At any point, if the student is experiencing difficulty, the assessor should allow the student to move ahead to the next question or stop altogether. There are many factors which may impact the performance of a student (e.g., acculturation process, performance anxiety, and subject specific language).Highlight importance of paying attention to these factors
13 Number Sense and Numeration Key mathematical number sense and numeration concepts in the primary assessments include:Quantity Relationships (composing and decomposing numbers - anchors of five and ten, subitizing, comparing and representing quantities)Counting (stable order, one-to-one correspondence, cardinality, conservation of number, movement is magnitude)Operational sense (addition and subtraction of single and double digit numbers, multiplication)Not an exclusive list…just some key mathematical concepts highlighted. These have been selected as the participants may not be as familiar with this mathematical content for teaching.
14 Composing and Decomposing Numbers Anchors of Five and Ten In the primary assessments, one of the required manipulatives is a ten frame. Ten frames can be oriented vertically or horizontally. In Ontario the ten frames is a tool that is embedded in many resources/guides. The ten frame (and there are five frames as well) allow student to compose and decompose number and relate these numbers to anchors of 5 and 10. These ten frames also encourage students to use “make ten” strategies when doing addition facts.Look at the grade two assessmentRefer to teacher/assessor guide – last page – question 8Note the use of the ten frame and look at Appendix A
19 Identifying a quantity without needing to count SubitizingIdentifying a quantity without needing to countA variety of manipulatives can be used to subitize. In the assessments, it is suggested that counters be used. The teacher/assessor should cover the counters as they put them down, and then uncover and recover (in other words, see if the student can identify without counting). Ten frames can be used, as well as dot plates (see the Guide to Effective Instruction NS and N primary for more information)
21 SubitizingWhat quantity did you see in the first dot configuration? What strategy did you use to determine the quantity?What quantity did you see in the second dot configuration? What strategy did you use to determine the quantity?
22 Counting Principles Some of the key counting principles include: stable orderone-to-one correspondenceCardinalityconservation of numbermovement is magnitude
23 Principles of Counting Stable Order Principle1,2,3,4,5,6…not1,2,3,4,6,8,9,10Stable Order Principle: Understanding that the counting sequence stays consistent. It is always 1,2,3,4,5,6, etc., not 1,2,3,4,6,8,9,10.Stable order means that a child must recite their counting words in a consistent and reproducible order. Children who miss numerals consistently or sporadically do not understand this Principle of counting.
24 Principles of Counting Order Irrelevance Principle6 in this group6 in this group1261354OR25643Order Irrelevance Principle: Understanding that the counting of objects can begin with any object in a set and the total will stay the same.When presented with a group of objects, children begin to count from one point, when they reach the final object they have counted the group. If asked “If you started at this point (a different one from the initial starting point), how many objects would you have?” the student should not need to recount.
25 Principles of Counting Conservation PrincipleConservation Principle: Understanding that the number of objects in a group stays the same no matter whether they are spread out or close together.In Piaget’s work with children, he would place a group of objects such as the first line of counters as shown on the slide and ask a child to count how many objects were in the group (“5”). He would then spread the objects out and not add any or take any away and would ask, “Now how many do you see?” He would be observing whether or not the child understands that the amount remains the same after he spread out the pieces. This is one stage of conservation. Another one is when the child can recognize that the two sets are the same if they see the one set spread out. If the two sets are spaced differently (and contain the same number) when the child first encounters them, they may not realize that they are the same. In this case look for the child to use the strategy of counting the two sets to determine whether they have the same number. If they don’t do this counting step and automatically assume that the longer line has more, they haven’t yet fully consolidated an understanding of conservation.If a child has developed the conservation concept of counting, they would be able to state that there were still 5 in the group and it wouldn’t matter that they were spread out. A child who has not developed this concept of counting would say that there are more in the second group.
26 Principles of Counting One-to-One CorrespondenceOne-to-One Correspondence Principle: Understanding that each object being counted must be given one count and only one count.In the early stages of development, it is useful for children to tag or move each item as it is counted.Tagging or moving the items provides visual cues to assist in counting.
27 Principles of Counting Cardinality Principle135724688 heartsCardinality Principle: Understanding that the last number of a count of a group of objects represents how many there are in the group.A child who recounts when asked how many candies are in the set that they have just counted does not understand the cardinality principle.In Arthur Baroody’s “Fostering Children’s Mathematical Power”, he states an example: instead of calling a collection of 12 blocks, “One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve,” we refer to it simply as “Twelve.”The Cardinality Principle implies that the last number in a count has special significance because it not only locates the last number counted, but it represents the total number of items in the collection. This is different from what children experience with letters. Letters stand alone; no more importance is given to the last letter in a sequence than to any other letter.One way to help children with cardinality is have the children count out objects (possibly as shown by the teacher on an overhead projector) and then the teacher covers those objects and asks, “How many are covered up? How do you know?”.
28 Principles of Counting Movement is Magnitude Principle42513Movement is Magnitude Principle: Understanding that as you move up the counting sequence, the quantity increases by one and as you move down or backwards, the quantity decreases by one. In skip counting, such as counting by 10’s, the amount goes up by 10 each time.This principle can be demonstrated using number lines (horizontal and vertical) and hundreds carpets and using quantities on the number line to demonstrate how each number goes up by one more etc.
29 Operational Sense What strategies could you use to find the sum? 83 + 8What strategies could you use to find the difference?Have participants do each question and share strategies with elbow partner. IN whole group share a few strategies. Talk about importance of allowing students to use alternative algorithms (emphasized in our curriculum document). We can assess more about their ns and n understanding by the strategies that they use.Note horizontal orientation of the questions…encourages students to use other possible algorithms
30 Number Sense and Numeration Key mathematical number sense and numeration concepts in the junior and intermediate assessments include:Quantity Relationshipsread, represent, compare and order whole numbers, fractions, decimalsOperational Sensesingle and multi-digit computation involving the four operations – increasingly focusing on multiplicative thinkingOrder of Operations (introduced in the grade eight (H) assessmentoperations with fractions, decimals, integers (in intermediate assessments)Proportional ReasoningRelationships between fractions, decimals and percentsNot an exclusive list…just some key mathematical concepts highlighted. These have been selected as the participants may not be as familiar with this mathematical content for teaching.
31 Quantity Relationships Form partners and/or triosEach group will need a copy of the grade seven (G) booklet and the accompanying teacher/assessor instruction bookletRead and discuss the following questions:1, 2, 3, 5, 6, 7,10, 12, and 13Use the grade seven assessmentHave participants form partners and/or triosInstruct participants to look at/discuss listed questions (all focusing on quantity relationships)Provide time (5-7) minutes for participants to read, discuss etc…Come back to whole group…Address general comments/questionsTake a closer look at questions 2 and 3 …and have participants share…what observations/assessment information do you anticipate you could obtain from these questions…what are observations that could be “look fors”Follow same procedure for questions 6 and 7
32 Read and discuss the following questions: Operational SenseContinue to work in partners and/or triosTask OneRead and discuss the following questions:4, 8, and 11Task TwoSelect one of the expressions in question 4. As a table group, use chart paper to show how many different ways you could find the answer. What manipulatives could help you? What manipulatives could help the students? Be prepared to share with our whole group.Re-connect back to the earlier conversation (when discussing primary assessments) about the importance of honouring/observing varying types of algorithmsProvide a piece of chart paper for each table..Each group (may be duplicates) selects a specific question…or presenter could assign questionsHow many ways could you find the answer? Show on your thinking on chart paper.What manipulative would you use to solve to complete this equation? What manipulatives should be accessible for students?***If possible, have base ten blocks available
33 Proportional Reasoning Read and discuss the following question:9What are some observations/assessment information you anticipate could be gathered from this question?Presenter to note the importance of using the visual information in the sample when working with the students. Also, it is always important to use the correct mathematical language with students. Instead of 46 over 100 we should say 46 one-hundredths (and not zero decimal four six!)
34 Using the Initial Mathematics Assessment Tool for English Language Learners, Grades K – 8 This tool is not intended to be a replacement for the ongoing assessment gathered by the classroom teacher. It is through a variety of assessment strategies and tools that the programming needs of all students are best addressed.Again, revisit this key idea…the ELL math tool is for one tool for gathering some initial assessment on newly arrived ELL students.
35 Our agenda…in reviewFocused Conversations about the ELL Math Assessment Tool including:Background information and overviewMaterials and organizationGuidelines for implementationMathematical knowledge/conceptsQuestions??Reconnect back to the key themes of the session….Provide an opportunity for questions….2