Teaching with Tasks - Mathematics Deia Sanders, Common Core Coach, Simpson County School District, Mississippi
PARCC Educator Leader Cadre Facilitator Notes Session Title Teaching Mathematics with Tasks Prerequisites N/A Target Audience Teachers, Curriculum Directors, and Administrators of grades 3-8 Mathematics Description In this workshop participants will learn how to align the tasks in their classroom with the higher order thinking skills required for college and career readiness. Participants will learn about the types of mathematics tasks on the PARCC assessment and their connection to the claims driving mathematics and standards for mathematical practices. As we prepare for the PARCC assessment we will want to begin creating tasks aligned to the modeling and reasoning requirements of the assessment. Participants will learn how to create and use tasks in formative assessments to make instructional decisions and study student's work as data. They will spend time reviewing actual student work samples and discussing the mathematics and mastery of the tasks. Participants will also learn about using performance tasks as summative assessments and the expectation of the PARCC assessment as a summative assessment. Participants will see a sample summative assessment task and discuss how to write these in to their own instruction. By the end of the session participants will work together to create both a formative and summative assessment for a CCSS mathematics standard. Objectives Participants will: Learn how teaching with tasks helps align the higher order thinking skills of the classroom to the assessments and real life situations. Materials/Resources Power Point Student work samples Sticky notes Evidence statement for standard selected for activity PLD for standard selected for activity Steps in Presentation Process Give PARCC information on tasks and claims. Review formative assessment and it's purpose, a way to design them, and an example. Participants will then complete a formative assessment and discuss their work. Next participants will work in groups to view and score student work samples of the same task.
PARCC Educator Leader Cadre Facilitator Notes Participants will then discuss summative assessments and PARCC as a summative assessment. They will then view an example summative task. You may have participants work through the summative task to discuss the different ways of solving and entering the problem if time permits. Review the differences and purposes in formative and summative assessments and answer any final questions before they are asked to create their own. In groups, participants will then be given a standard and they will work together to create a formative and summative assessment task.
Teaching Mathema-cs with Tasks Goal Create the alignment of teaching, learning, and assessment of higher order thinking skills, and their transfer them to real life situa;ons. 2 PARCC Tasks 1
Claims Driving Mathema-cs Master Claim: On- Track for college and career readiness. The degree to which a student is college and career ready (or on- track to being ready) in mathema;cs. The student solves grade- level /course- level problems in mathema;cs as set forth in the Standards for Mathema;cal Content with connec;ons to the Standards for Mathema;cal Prac;ce. Sub- Claim A: Major Content 1 with Connec-ons to Prac-ces The student solves problems involving the Major Content 1 for her grade/course with connec;ons to the Standards for Mathema;cal Prac;ce. Sub- Claim B: Addi-onal & Suppor-ng Content 2 with Connec-ons to Prac-ces The student solves problems involving the Addi;onal and Suppor;ng Content 2 for her grade/ course with connec;ons to the Standards for Mathema;cal Prac;ce. Sub- Claim D: Highlighted Prac-ce MP.4 with Connec-ons to Content (modeling/ applica-on) The student solves real- world problems with a degree of difficulty appropriate to the grade/course by applying knowledge and skills ar;culated in the standards for the current grade/course (or for more complex problems, knowledge and skills ar;culated in the standards for previous grades/courses), engaging par)cularly in the Modeling prac)ce, and where helpful making sense of problems and persevering to solve them (MP. 1),reasoning abstractly and quan;ta;vely (MP. 2), using appropriate tools strategically (MP.5), looking for and making use of structure (MP.7), and/or looking for and expressing regularity in repeated reasoning (MP.8). Sub- Claim C: Highlighted Prac-ces MP.3,6 with Connec-ons to Content 3 (expressing mathema-cal reasoning) The student expresses grade/course- level appropriate mathema;cal reasoning by construc;ng viable arguments, cri;quing the reasoning of others, and/or arending to precision when making mathema;cal statements. Sub- Claim E: Fluency in applicable grades (3-6) The student demonstrates fluency as set forth in the Standards for Mathema;cal Content in her grade. 4 Preparing for PARCC Major, Additional, and Supporting Standards Connections to Standards for Mathematical Practice Computations Modeling and Reasoning Tasks 2.5 minutes per point 5 Forma-ve Assessment Using student work as data Not scoring Evidence of learning Meet immediate needs of students 2
The process of studying student work is a meaningful and challenging way to be data- driven, to reflect cri;cally on our instruc;onal prac;ces, and to iden;fy the research we might study to help us think more deeply and carefully about the challenges our students provide us. Rich, complex work samples show us how students are thinking, the fullness of their factual knowledge, the connec;ons they are making. Talking about them together in an accountable way helps us to learn how to adjust instruc;on to meet the needs of our students. - Annenberg Ins;tute of School Reform Forma;ve Task Consider a ramp design Entry level Core of instruction Extension Example Forma-ve Task Three students bring 4 pencils each. Draw an array to show how many pencils they have altogether. If each pencil cost $.10, how much did each student spend on their pencils? How much did they spend altogether on pencils? If they have $2.00, how many more pencils can they buy? If they bought the same amount of pencils and spent $3.90 altogether, how many pencils did each student get? 3
Comple-ng a task Complete the task on your own. Discuss the mathema;cs involved in the task. What skills or standards did you use? Analysis of Student Work Tells: Where the learner is Where the learner is going How the learner can get there Purpose Examine understanding Examine misconceptions Find potential Deepen understanding Develop problem solvers 4
Review of student work Review student work Decide score Place score on sticky note Fold sticky note so next reviewer can t see previous scores Summa-ve Tasks About 1/3 of points come from Type II and III tasks Modeling and reasoning Real world Multiple standards Can be messy Example Summa-ve Task A student goes shoe shopping over spring break. She has two different coupons to use on the shoes she wants to purchase. When she gets to the store they tell her she may only use one coupon. The original cost of one pair is $65.00 The original cost of the other pair is Coupon A $44.00. Coupon B Buy first pair at original price and get second pair of equal or lesser value at 75% off 35% off entire purchase What is the cost when using Coupon A? Which coupon should the student use? Justify your reasoning. 5
Forma-ve vs. Summa-ve Formative Informs decisions Ramp design Can assess individual skills Summative Assessing for mastery Multiple entry points Assess multiple skills Crea-ng A Task 6.NS.8 Solve real- world and mathema-cal problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Resources: Standard Personal Experience Evidence Statement PLD 17 Conclusion Students need opportuni;es to solve tasks Teachers can target instruc;on based on tasks results If we do not prepare our students with tasks their successes will be limited 18 6