Mathematics

The (DOC) Thinking Through a Lesson Plan Protocol (TTLP) is used to guide teachers to think deeply about a specific lesson that will be taught. The goal is to move beyond a basic lesson plan to a deeper consideration of how to advance students’ mathematical understanding during the lesson.

Part 1 of the TTLP lays the groundwork for planning before the implementation of the rich math tasks in the classroom. First, identify the learning targets of the lesson. Then, select a (PDF) high cognitive demand math task aligned to the learning targets from the district’s textbook resource. Next, determine how to launch the task to help students make sense of problem. For example, determine how to activate prior knowledge, make sense of the task and decide which instructional tools will be made available to the students.

Part 2 of the TTLP helps monitor students as they engage in the task during the Explore Phase. Prior to implementing the math task, anticipate strategies and misconceptions students may encounter while solving the task. Based on anticipated strategies, formulate questions ahead of time to clarify and assess student thinking. The rest of the (DOC) monitoring tool can be completed during the Explore Phase while monitoring and recording the names of students using the anticipated strategies. The monitoring tool will help in selecting and sequencing the students who will share their thinking in the Summarize Phase.

Part 3 of the TTLP focuses on how to orchestrate a whole-group discussion of the task. This discussion uses the different solution strategies produced by students to highlight the mathematical ideas that are the focus of the lesson. Strategically plan the order in which solutions are presented to help develop students’ understanding of the mathematical ideas. In addition, develop questions to ask to make connections between students’ strategies. Read (PDF) Thinking Through a Lesson Protocol: Successfully Implementing High-Level Tasks to dig deeper.

“Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and argument.” (Huinker & Bill, 2017).

Teachers need to establish (PDF) norms for discourse to create a safe environment and ensure equitable participation. (DOC) Productive talk moves can be used by teachers to engage all students in discussion. Teachers need to think about the goal they are trying to reach based on student responses. Think about the following goals and you determine which talk move to use during discussion.

• Helping Individual Students Clarify and Share their Own Strategies
• Helping Students Orient to the Thinking of Other Students
• Helping Students Deepen their Reasoning
• Helping Students to Engage with the Reasoning of Other

(URL) Inside Mathematics 

Taking Action:  Implementing Effective Mathematics Teaching Practices (K-5)
ISBN-13: 978-0873539692

Taking Action:  Implementing Effective Mathematics Teaching Practices (6-8) 
ISBN-13: 978-0873539753

Taking Action:  Implementing Effective Mathematics Teaching Practices (9-12)
ISBN-978- 0-875353-976-0

Children's Mathematics:  Cognitively Guided Instruction (Whole Number Operations)
ISBN-13: 978-0325052878

Extending Children's Mathematics:  Innovations in Cognitively Guided Instruction (Fractions and Decimals)
ISBN-13: 978-0325030531
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Assessment to Inform Instruction supports teachers in answering the question What comes next in learning?

Among the various methods of assessment for learning are listening to student contributions (both responses and questions students ask to the teacher and of their peers) and analyzing their written work and using that information to interpret student understanding and determine next steps in instruction. An image of student work below shows that the student recognizes there are 16 ounces in a pound and that this problem is multiplicative in nature and that the student has an algorithmic method for solving 16 x 5, as opposed to other methods, such as counting by 5s or using repeated addition.

In elementary mathematics, researchers have developed progressions that describe the likely development of student mathematical thinking for a given concept, what we call big ideas in mathematics.  For example, addition and subtraction and multiplication and division are big ideas in mathematics. These progressions can guide teachers in making instructional decisions based on a student’s progress as compared to the progression.  Below are progressions for grades Kindergarten through Fifth Grade whole number concepts.

Example of a Progression for Addition and Subtraction

Example of a Progression for Multiplication and Division 

Diagnostic Assessment can be used to identify a students’ strengths as well as areas for improvement, can form the basis for interventions and is often shared with multiple educators in order to plan supports to improve the student’s learning.  This short interview-based assessment provides the teacher with information related to the students’ understanding of number, addition and subtraction, place value, and multiplication and can be used to determine if the student is performing at grade level as well as to determine areas of strength or weakness. 

Interim (Unit) Assessments support teachers in answering the questions Which standards are our students consistently not mastering? Where can we improve instruction? Which students need specific help? (Stiggins, 2010).  

Interim assessments should identify content standards that students are struggling to master as well as the students struggling to meet those standards. Teachers can use this information to improve their own instructional practices aimed at those standards. Additionally, these assessments can help teachers and students focus on identifying student strengths and areas of improvement so they can intentionally plan interventions.

Assessment of Learning supports teachers, schools, and districts in answering the questions What standards are our students consistently not mastering?  Where and how can we improve instruction next year? (Stiggins, 2010).  

Summative assessments evaluate student learning against intended outcomes. These assessments provide evidence of student achievement and can identify the percentage of students meeting performance expectations on state content standards (Chappuis, 2015).

In Michigan, students are assessed summatively in the spring of each year, starting in 3rd grade.  MDE houses sample assessment items for 3rd - 7th grade M-STEP 

Secondary students are assessed using the PSAT or SAT.  Released items can be used in a variety of ways to inform the work that students are doing in the classroom.  

 The Formative 5:  Everyday Assessment Techniques for Every Math Classroom (Fennell, Kobett, & Wray) ISBN-13: 978-1506337500         

Teaching Number in the Classroom for 4-8 year olds (Assessment and Intervention) ISBN-13: 978-1446282694

Developing Number Knowledge: Assessment, Teaching, and Intervention with 7-11 year-olds ISBN-13: 978-0857020611