Glad to have you back! Today we continue our book study of Teaching Student-Centered Mathematics PreK-2 by Van de Walle, Lovin, Karp, and Bay-Williams with a discussion of chapters two and three. Please feel free to leave a comment, as we would love to hear your thoughts about the chapters and what they mean to you as a teacher and your students as learners.
Chapter 3: Assessing for Learning
The authors begin chapter three by stressing that assessment should not be separate from instruction. Assessment for learning is ongoing and is a means of informing future instruction. As teachers, we need to do all we can to assess what students are able to do in order to make necessary instructional decisions. Our students also become empowered when we share with them our assessments of their learning and how they are capable of growing (comparing themselves to where they were and how far they have come, not comparing themselves to their classmates).
I love how the authors created analogies for formative and summative assessments. Formative assessments are “streaming videos” that capture a child’s thinking over time. A summative assessment is a “digital snapshot” of a child’s learning at one moment in time. Formative assessments are assessments for learning.
Observations are HUGE! I would have to say that 80 percent of the assessment I do for learning comes from observation. Observations of EVERYTHING! Small guided math groups provide an intimate opportunity for me to observe students as they problem solve, create meaning, share their thinking, and justify their solutions. I gain great insight into each child’s understanding of important concepts as well as any misunderstandings they may have. During mini lessons and number talks, students’ talk surrounding a concept, strategy, or activity provides important insight as well. I also gain a great deal of insight as students solve problems in pairs (typically in their math journals) and by talking with students one-on-one.
The authors suggest some ways of recoding observations that we are most likely familiar with; anecdotal records, checklists, and questioning. A couple tips form each are helpful to me:
- Anecdotal records – I don’t need to record observations on everyone in one day. I can choose just a few.
- Checklists – I can create checklists for “big ideas” and conceptual understanding (for individual students) or those that show the whole class’ understanding on a one-page checklist.
- Questioning – I can ask specific questions and record observations of specific students as I circulate the classroom.
Tasks are another great way to assess students. After reading the components of “good” tasks and the examples presented by the authors, this is something I do a lot. Simply presenting students with a word problem and asking them to explain their thinking, and justify their answer after solving, can serve as an assessment. Tasks can come in various forms. Those that require students to explain their thinking and represent their understanding in multiple ways are especially powerful.
The end of the chapter addresses rubrics and how they can be used by teachers and students to assess learning. I think one of the most important things to consider when using rubrics is that the students are able to see what is expected–the level of performance for which to aim. As the authors state, “A rubric is much more than a grade. It is a meaningful way to communicate feedback to children (and parents). It should let children know how well they are doing and encourage them to work harder by giving specific areas for improvement.” Rubrics can be created in many forms, from the self-evaluation of a student’s understanding using pictures and short phrases to a four point rubric that rates a student’s understanding from unsatisfactory to excellent (with specific indicators of each). Like any other formative assessment, rubrics need to provide information necessary for making instructional decisions and help students to grow. When I taught fifth grade, we used a lot of rubrics and kids had input into creating them, but as a second grade teacher I rarely use them. Yet, the rubrics presented in this chapter have opened my eyes to some new possibilities for using rubrics with younger students.
Chapter 4: Differentiating Instruction
Differentiation is essential! I decided to pull some ideas from the chapter I feel best illustrate what we as teachers need to know in order to best meet our students’ needs.
We need to…
- Know our kids. — What is their current knowledge/understanding? What are they interested in? How do they learn best? (readiness, interest, and learning profile). We will differentiate according to these three.
- Know what we will differentiate to best help our students learn. — Should we differentiate the content, product, process, and/or learning environment? Each of these is explained in detail.
- Know how to differentiate. Will we tier instruction, use parallel tasks, provide differentiated learning centers, meet with small flexible groups, etc?
I appreciate how the authors show the simplicity of tiering a task/problem. It was done by simply adjusting the numbers in the problem from single-digit addends that would add to less than ten, single-digit addends that would add to greater than ten, and double-digit addends. The addition of two addends and the context remained constant in each problem, but the level of difficulty was increased/decreased by adjusting the numbers. This is something I often do with journal problems that students work on independently or with a partner during guided math rotations. I number baggies that contain the problems (2 or 3 depending on students’ needs). Parallel tasks are similar in that all tasks are focused around the same central idea but at different levels. After completing parallel tasks, students can then come together to discuss their thinking no matter which task they worked on. For example, comparing two quantities to find the difference may be the focus, yet the tasks/problems are different.
Learning centers are another great way to differentiation independent practice during guided math rotations. Our learning centers are differentiated and organized for students to easily access during independent work time. Differentiated centers help students to build confidence and are designed to be engaging.
Something I would like to incorporate more this coming school year are open questions. Open questions are those that elicit a number of correct solutions. These types of questions/problems, in themselves, lend to natural differentiation as students bring with them different levels of understanding to solve the problems in multiple ways.
Ultimately, the framework of guided math is designed to provide for differentiation. The intimacy of these small groups foster accountability and confidence and provide the support students need to grow.
To end with, I would like to share just a couple of formative assessment checklist you might find useful. If you end up using any of these, I would love to hear how they worked for you and your students.
Money Performance Assessment Checklist
For this assessment, students were individually assessed over the course of several days. Students were given coins during the assessment to help me understand which skills they had necessary to work toward the second grade measurement standard printed at the top of the checklist. The information gathered with the checklist helped to inform guided math groups. As you can see from the pic, there was a wide range of understanding.
Odd/Even Performance Assessment Checklist
This assessment was done similar to the money assessment, yet it was an assessment used after we had been exploring counting objects to 20 by 2 and using various strategies to determine if a number is odd or even. It was a quick assessment that was done over several days. Students were required to explain how they knew a number was odd/even. Counters and paper were provided as many students chose to use models and words to show their understanding.
Please feel free to share your thoughts and ideas related to chapters 3 & 4 in a comment. AND don’t forget to visit our fellow bloggers participating in the book study by clicking on the links below!
ALSO–Before you head out, I encourage you to head on over to The Teacher Studio to read a wonderful interview with Laney Sammons, author of Guided Math: A Framework for Mathematics Instruction! You don’t want to miss it!
We will see you back here on Sunday for chapters 5 & 6!