Math Garden



Name of Teacher: School:HCPSS Student Learning ObjectiveMathematical Practices 7 & 8: Seeing Structure and Generalizing (Content Focus)ComponentDescriptionStudent Learning Objective (SLO)100% of students will demonstrate growth in Common Core State Content Standards for Mathematics with connections to the Standards for Mathematical Practice (Practices 7 and 8: Seeing structure and generalizing), as evidenced by performance on worthwhile mathematical tasks and/or high quality formative assessment items and participation in effective classroom discourse.PopulationOf the ______ (number) students selected for this SLO:______ performed at the (low/high) basic level on the previous year’s (M/H)SA______ performed at the (low/high) proficient level on the previous year’s (M/H)SA ______ performed at the (low/high) advanced level on the previous year’s (M/H)SA ______ were below grade level at the end of the previous year______ were on grade level at the end of the previous year______ were above grade level at the end of the previous year.Learning ContentThe Standards for Mathematical Content are a balanced combination of procedures and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices (CCSSO, 2010).The Standards for Mathematical Practice describe varieties of expertise that mathematics teachers should seek to develop in their students. Taken together, practices 7 and 8 (below) describe the practices that fall under seeing structure and generalizing. Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with Mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.Those content standards, which set an expectation of understanding, are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice.Instructional IntervalSchool year 2013-14 (one year)Mathematics classes are 50 minutes per day, 5 days per week. (Seminar periods provide an additional 50 minutes per day, 5 days per week.)Evidence of GrowthTo monitor student progress, the following data/measures will be used:Analysis of student work samples to identify their level of conceptual understanding, procedural fluency, productive disposition, strategic competence, and adaptive reasoning (National Academies Press, 2001).Analysis of student behaviors and dispositions outlined in the Standards for Mathematical Practices (Seeing structure and generalizing, MP#7 and MP#8) during classroom learning experiences.Teachers should utilize the Mathematical Performance Rubrics as tools to guide task selection, to guide lesson design, and to inform growth in content.BaselineUsing the Student Implementation Rubric, of the ______ (number) students selected for this SLO baseline levels of performance with identified content______ % earned a student implementation score of 4 ______ % earned a student implementation score of 3______ % earned a student implementation score of 2______ % earned a student implementation score of 1(Attach class roster to share students’ scores on Beginning-of-the-Year Assignment/Performance Task/Assessment.)Rationale for Student Learning ObjectiveThe abilities and mathematical dispositions of students develop as to learn are provided and are described in the Student Implementation Rubric. As a means to help students continue in a pattern of growth with mathematical proficiency, the rubric is a tool to help consider and gauge students’ progress with performance on tasks/formative assessments. With teacher guidance, students’ proficiency will progress from the baseline levels to more advanced proficiency levels.Target The target for the _____ students identified for this SLO will be to demonstrate an increase in mathematical content proficiency level(s), with a focus on practices 7 and 8, using the Student Implementation Rubric.*Please note: Students identified by IEP teams as having significant cognitive disabilities will have individual targets.Criteria for Effectiveness(Mathematical Practices 7 and 8)Full Attainment of TargetPartial Attainment of TargetInsufficient Attainment of TargetMore than 90% of students earn a student implementation score of 3 or 4 (using the Student Implementation Rubric).Between 75% and 90% of students earn a student implementation score of 3 or 4 (using the Student Implementation Rubric).Less than 75% of students earn a student implementation score of 3 or 4 (using the Student Implementation Rubric).Strategies The teacher, working with a collaborative team, should collect data through informal observation, student work samples on worthwhile mathematical tasks and formative items, and other learning artifacts (including digital recordings, student responses to higher order thinking questions). Using the Student Implementation Rubric, record SLO baseline levels of performance with identified contentIn planning learning opportunities for students to engage in the mathematical content, teams should:Identify content to be taught.Consider what mathematics students are to know and how students can best demonstrate understanding.Select mathematical tasks/formative items that provide students with opportunities to engage in collaborative critical thinking, productive student-to-student discourse with a focus on content vocabulary and literacy, multiple solution pathways and representations, and productive struggle. Use the Task/Formative Assessment Design Rubric to evaluate the potential of the tasks/items in supporting the development of mathematical content and mathematical practices.Carefully consider the strategies needed to help students engage in productive reasoning and sense making. (e.g., initiating think-pair-share, think-aloud, questioning and wait time, grouping and engaging problems/tasks, using questions and prompts with groups, allowing students to struggle, etc.)Formulate several questions they can pose to students to promote reasoning, sense making and communication. Consider possible student responses and common student understandings and approaches for addressing student misunderstandings.Clarify and refine formative/summative assessment activities.Sequence lesson experiences to maximize opportunities to engage in problem solving. Strategically plan supports offered to students so that students engage in productive struggle without becoming overly frustrated.For selected content, collect evidence and data throughout the school year to reflect on individual student understanding and growth with content and practices. Evidence should be collected at least twice per unit. Evidence could include, but is not limited to: student work samples, digital recordings, and feedback from peer observation, and/or a teacher’s classroom observations.Mathematics Performance Rubrics – Seeing Structure & Generalizing (Content Focus)Rubric 1 – Task/Formative Assessment Design4The task/item has the potential to engage students in exploring and understanding the nature of mathematical concepts, procedures, and/or relationships, such as:Doing mathematics: using complex and non-algorithmic thinking (i.e., there is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instruction, or a worked-out example); ORProcedures with connections: applying a broad general procedure that remains closely connected to mathematical concepts.Connections between mathematical practices and content: meaningfully connect content standards and mathematical practices.The task/item must be designed to elicit evidence of student’s seeing structure and generalizing. For example, the task/item MAY require students to:Look for patterns or structure, recognizing that quantities can be represented in different waysRecognize the significance in concepts and models and use the patterns or structure for solving related problemsView complicated quantities both as single objects or compositions of several objects and use operations to make sense of problemsNotice repeated calculation and look for general methods and shortcutsContinually evaluate the reasonableness of intermediate results (comparing estimates), while attending to details, and make generalizations based on findings.The task/item explicitly prompts for evidence of students’ reasoning and understanding.The task/item allows for multiple solutions and/or multiple strategies to solve.3The task/item has the potential to engage students in complex thinking or in creating meaning for mathematical concepts, procedures, and/or relationships. The task/item must be designed to elicit evidence of student’s seeing structure and generalizing. For example, the task/item MAY require students to:Look for patterns or structure, recognizing that quantities can be represented in different waysRecognize the significance in concepts and models and use the patterns or structure for solving related problemsView complicated quantities both as single objects or compositions of several objects and use operations to make sense of problemsNotice repeated calculation and look for general methods and shortcutsContinually evaluate the reasonableness of intermediate results (comparing estimates), while attending to details, and make generalizations based on findings.However, task/item does not warrant a “4” because: The task/item does not explicitly prompt for evidence of students’ reasoning and understanding.Students may be asked to engage in doing mathematics or procedures with connections, but the underlying mathematics in the task is not appropriate for the specific group of students (i.e., too easy or too hard to promote engagement with high-level cognitive demands);There are limited strategies to solve the problem.2The potential of the task/item is limited to engaging students in using a procedure that is either specifically called for or its use is evident based on prior instruction, experience or placement of the task. There is little ambiguity about what needs to be done and how to do it. The task/item does not require students to make connections to the concepts or meaning underlying the procedure being used. Focus of the task/item appears to be on producing correct answers rather than developing mathematical understanding (e.g., applying a specific problem solving strategy, practicing a computational algorithm).1The potential of the task/item is limited to engaging students in memorizing or reproducing facts, rules, formulae, or definitions. The task does not require students to make connections to the concepts or meaning that underlie the facts, rules, formulae, or definitions being memorized or reproduced.Rubric 2: Student Implementation4Student-work indicates the use of complex and non-algorithmic thinking, problem solving or exploring and understanding the nature of mathematical concepts, procedures, and/or relationships Student-work indicates evidence of at least three of the behaviors defined by student’s seeing structure and generalizing; Look for patterns or structure, recognizing that quantities can be represented in different waysRecognize the significance in concepts and models and use the patterns or structure for solving related problemsView complicated quantities both as single objects or compositions of several objects and use operations to make sense of problemsNotice repeated calculation and look for general methods and shortcutsContinually evaluate the reasonableness of intermediate results (comparing estimates), while attending to details, and make generalizations based on findings.Student work includes an accurate and mathematically sound solution that reflects a deep, conceptual understanding for procedural fluency.3Student work indicates that students engaged in problem-solving or in creating meaning for mathematical procedures and concepts BUT the evidence of students thinking or reasoning is incomplete (no explanation, justification, or explicit connections).Student-work indicates evidence of at least two of the behaviors defined by student’s seeing structure and generalizing (see above); Student work may or may not include an accurate and mathematically sound solution that reflects a deep, conceptual understanding for procedural fluency. (For example; solutions developed by procedures without connections OR an incorrect solution with minor flaws)2Students engage with the task/item at a procedural level. Students apply a demonstrated or prescribed procedure. Students may be required to show or state the steps of their procedure, but are not required to explain or support their ideas. Students focus on correctly executing a procedure to obtain a correct answer.Student-work indicates evidence of no more than one of the behaviors defined by student’s seeing structure and generalizing (see above); Student work may or may not include an accurate solution that reflects procedural fluency. (For example; solutions developed by procedures without connections OR an incorrect solution with major flaws)1Students engage with the task/item at memorization level. Students are required to recall facts, formulas, or rules (e.g., students provide answers only), OREven though a procedure is required or implied by the task/item, only answers are provided in students’ work; there is not evidence of the procedure used by the students.Student-work indicates no evidence of the behaviors defined by student’s seeing structure and generalizing (see above); Student does not include an accurate and mathematically sound solution that reflects a deep, conceptual understanding for procedural fluency. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download