Overview

Session Focus

Reset

In this session you will consider ongoing assessment for learning and its impact on instruction. You will watch teachers as they assess their students’ understanding in different settings –playing a game, solving a problem, during a whole group share and by looking at their written work. You will consider what a teacher can learn through these interactions that informs their teaching and reflect on your own teaching practices.

In mathematics, as in any subject, teachers continually assess students’ strengths and needs and think through how best to accommodate differences to involve all students in substantive and challenging work. All students should be expected to achieve at high levels and to master more efficient strategies.

One way to think about high expectations for all students is to appreciate and acknowledge where a child currently is, and to figure out where you want her to go and how you can help her get there. To accomplish this, teachers must:

• Know the curriculum. Study how the mathematical ideas build over many lessons. Take the time to understand the mathematics focus in each unit and of each lesson.
• Know the mathematics. It’s important to understand how mathematical concepts ideas develop across the grades. Develop a solid understanding of mathematics content, how students learn, and effective, age appropriate pedagogy.
• Know the students. Observe students at work, listen to their discourse, and develop an understanding of their mathematical ideas by analyzing what they say and do.

• Have a plan. To find out what students are doing, and find examples of different strategies to share during the discussion, having a ‘game’ plan is key.
• Establish classroom norms early on. Students work independently alone or in groups, they are expected to communicate their reasoning and listen to that of others, and they see mistakes as opportunities for learning. The environment is one where students can take risks and learn.
• Ask questions that push students to explain their solution, clarify their thinking, or uncover a mistake.

Read Formative Assessment (NCTM)

How are summative and formative assessments different?

Formative assessments help the teacher learn what students know and understand – a snapshot in time. This information enables the classroom teacher to make appropriate instructional decisions and provide tangible feedback to students during learning. Students can also self assess and play an active role in their learning.

Getting Started: Assessing in the Moment

Teacher observations are an important part of ongoing assessment. Although individual observations may be little more than snapshots of a student's experience with a single activity, when considered together over time, they can provide an informative and detailed picture. These observations can be useful in documenting and assessing a student's growth and offer important sources of information when preparing for family conferences or writing student reports.

Before the lesson, review the lesson and consider what you want to learn about your class or a group of students. Identify a focus and a few questions you think about as you observe. Example: “What strategies are the students using?” As you observe you may use or rephrase the focus question to ask students to clarify or better what they are doing and thinking. Examples: “What strategies are you using?” “Show me how you solved the problem.”

Decide how you plan to record and keep track of your observations of students. The most important aspect of a record-keeping system is that it be both manageable and useful for you. Some teachers:

• Jot down observations of students’ work on a class list of names. Because the space is somewhat limited, it is not possible to write lengthy notes; however, when kept over time, these short observations provide important information.
• Place stick-on address labels on a clipboard. Take notes on individual students and then peel these labels off and put them in a file for each student.
• Jot down brief notes at the end of each week. Some teachers find that this is a useful way of reflecting on the class as a whole, on the curriculum, and on individual students. Planning for the next week's activities can benefit from these weekly reflections.
• Use technology such as a camera, smartphone, tablet or audio to document students as they work. The advantage of documenting is that you can review the student working at a later time. Most schools require parental permission to record students.
• Collect portfolios that might include observation checklists, digital recordings of students at work, student work on written assessments, and other examples of students’ written work.

The second grade teacher in this video describes what he does to informally assess students as they work.

Activity 1: Observing Students - Listening and Noticing

In this activity you will watch teachers assess in three different settings – during a game, as students work independently on a problem and in a small guided group setting. The students are engaged in their regular math work of the day. These teachers represent different grades, different settings, different situations, and they have different goals. Still you will notice some commonalities.

You will do some math and predict how students might approach the same tasks before you watch the video clips. As you engage in the math activities and watch the classroom video clips, think about:

• the math the students are working on
• anticipate what they might do and say
• how you would support their learning

In this game, students roll a 6 to 12 number die and a 1 to 6 dot die to generate subtraction problems. They record the difference on their gameboard.

Read: Subtraction Roll and Record Directions

Read: Ongoing Assessment: Observing Students at work

   

Part 4: Looking for Commonalities

Notebook

In your notebook, describe the commonalities you observed among the three teachers and students. If you want to revisit the video clips, use the links below.

 

Teacher observations are an important part of ongoing assessment. Individual student observations are snapshots of that student's experience with a single activity. Over time, they provide an informative and detailed picture.

A classroom culture where students work in pairs, groups, and independently allows the teacher to observe students working in different ways. This culture must be established at the beginning of the year.

Points to consider when making observations:

• Do the math and think about strategies that may come up ahead of time – this is key to making sense of what students understand and what they don’t yet understand
• Classroom management – students working independently, no interruptions – allows you to observe them
• Observations are a time for understanding; not for teaching
• Decide on 4 or 5 students to observe and make a note about each one; do this repeatedly over the week to get a picture of your whole class
• Not sure what to ask? Start with, “How did you know?” or “What was your first step?”

Activity 2: Watching and Listening to Students at Work

In this activity, you will experience two first grade experiences, both are focused on adding by groups.

• In the first experience will watch students as they share their work and consider what you learned from the students’ verbal descriptions.
• In the second experience, you will match a set of student work with written descriptions of what the students did and said as they organized a set of squares. After you match the students with their work, you will pair students based on what you’ve learned.

Final thoughts…

The information from the written work without observing students as they work shows only part of students’ understandings and misunderstandings.

Activity 3: Looking at Student Work Using a Rubric

Find the Product of Two 2-Digit Numbers

The following multiplication problem is part of an End-of-Unit Assessment in Investigations. Students have engaged in similar work throughout the unit. The Math Focal Points of the class work are solving 2-digit by 2-digit multiplication problems, breaking up multiplication problems efficiently, multiplying fluently by multiples of 10 and using clear and concise notation. For this assessment, students work independently to solve this problem.

 

may show evidence of understanding the problem

DIET Protocol

Students communicate their thinking through verbal descriptions, demonstrations with tools, written work and a combination of all three.

Read DIET protocol

Notebook

In your notebook, describe how the rubric helped you look at the student work.

Discussion

Share two things about assessment for learning you are taking away from this session. Be specific.

• Remember to participate in and return to the Discussion Forum conversations you and other participants have initiated.

Go to the Forum

Notebook

Complete the Session 3 Notebook page using the indicated prompts.

In the final field of your notebook, reflect on the key take-aways from this session for your own learning and record ideas that you will implement to support math learning.

• Go to Notebook

Key Learnings

Assessment for learning involves:

• checking to see what has been learned and what needs to be learned next
• engaging students in assessing their learning and the learning of others
• setting transparent kid friendly learning targets for students
• knowing the learning paths and the critical learning targets along the way depending on their needs

In order for productive assessment to be an integral part of student learning and instructional planning, teachers need to:

• create a classroom culture where assessment is a natural part of learning
• know the math and how it’s presented to the students at different grade levels
• figure out what students understand so you can plan appropriate next steps
• scaffold instruction and discussions to make them accessible to all
• plan guided group instruction with a targeted goal for all students
• ask questions that probe students’ thinking
• listen to students’ reasoning as they work
• notice what students do and how they communicate their ideas
• believe assessment is an ongoing process rather than an event