Chapters 5 & 6 are the focus of today’s discussion of Teaching Student-Centered Mathematics PreK-2 by Van de Walle, Lovin, Karp, and Bay-Williams. To read past chapter discussion for this book study, visit our book study archive.
Chapter 5 – Planning, Teaching, and Assessing Culturally and Linguistically Divers Children
“Instead of teaching English language learners (ELLs) from a deficit model (lack of knowledge and experience), we can connect their experiences from home and family to that of the mathematics classroom. The more we enhance learning for all children, regardless of thier places of birth, the more enriched the opportunities for learning become.”
At the end of the chapter, the authors ask a “Stop and Reflect” question about what things I would put on my list of to dos for culturally and linguistically diverse students. Therefore, I picked the following from the chapter as things that I can do, or already do, that will/do benefit English language learners in my classroom; differentiating, helping students develop academic vocabulary in multiple ways, and providing a positive environment for sharing.
The authors begin the chapter by addressing mathematics as a language, not a universal language in all aspects as it is often referred. Not having a great deal of experience with English language learners, I found the discussion of how procedures in mathematics differ in many countries to be fascinating, specifically mental mathematics. If faced with a student who has an alternate approach to mathematics, the authors suggest asking children to explain in detail how they solved a problem and to share their thinking with other students. This lets the student who uses an alternate method know that there thinking is valued.
Differentiation is important for culturally and linguistically diverse students, but this needs to be done without assuming that these students have little understanding or experience. Something as simple as putting a problem in a familiar context can serve to remove language barriers and keep focus on their reasoning and the “big idea”. Using visuals, simplifying sentences, and eliminating confusing vocabulary are all considerations when designing problems.
Helping culturally and linguistically diverse students develop academic vocabulary was a great focus of chapter 5. I appreciated the section related to explicitly teaching math vocabulary–something important for all students. Love the following suggestions of activities to reinforce math vocabulary:
- picture dictionaries that illustrate concepts
- vocabulary games
- interactive word walls (with illustrations and translations)
As with all students, a positive learning environment that instills risk taking, multiple representations, and an acceptance of multiple ways of knowing is essential. When it comes to discussion/sharing, the authors give some great tips for making the process positive for culturally and linguistically diverse students:
- use gestures and visuals important to learning
- revoice, or restate, using appropriate language as related to concepts
- give ample time to communicate ideas, don’t rush
- ask questions that press for detail that creates understanding for yourself and other students
- allow culturally and linguistically diverse students time to share their thinking (may be unique) with other students
Many of the above are also important to keep in mind when assessing students’ understanding.
Chapter 6 – Planning, Teaching, and Assessing Children with Exceptionalities
Many moons ago, I began my journey in education as a regular education and special education major. I made the decision to focus on both because I knew I would be faced with a diverse collection of learners. I wanted to meet their needs to the best of my ability. From my early experiences in college, I was exposed to a variety of needs that I would be charged with meeting in my own classroom; not just the needs of those who struggle academically. I also encountered students who were gifted, those whose behaviors impeded their learning, and those whose efforts were so poor that it was questionable as to whether their teachers would move them on to the next grade. Having experienced this early, and being thrust into a diverse and challenging population of learners my very first year of teaching, I feel I am all the better for it. I developed a strong philosophy early on–one that continually reminds me that I must strive to do my best for all learners. I feel the topics of these beginning chapters to blend together, in a sense, because they help us teach all students for understanding.
In this chapter, the authors address Response to Intervention (RTI), students with learning disabilities, students with moderate or severe disabilities, and those that are mathematically gifted. I chose to pull a few things I feel especially helpful/important…
Concrete, Semi-Concrete, Abstract (CSA)–Often referred to as Concrete, Representational, Abstract (CRA)
This instructional model is one I learned in college and was expected to use in lessons early. It begins with the use of tools/manipulatives to solve problems, moves to representation using drawings and pictures, and finally the use of only numbers, symbols, and/or mental thinking. I think the most important thing to remember is that students are not held back from reaching the abstract stage until they are “ready”. In solving any problem, students should be taken through all three stages so they can make a strong connection between models and the accompanying numbers and symbols.
During a think aloud, the teacher models the steps to complete a task while sharing his/her thinking out loud. The student/s have a parallel task and follow the teacher by imitating the process of talking through their solution. The authors remind us to assess the needs of students in order to begin where their thinking lies rather than simply relying on what we think to guided us. While we are providing a needed guide for students to help develop understanding, it is equally as important to instill in our students that they “must eventually learn to create a path to new learning on their own.”
Dos and Don’ts for the Mathematically Gifted
Do (when appropriate):
- Accelerate: A student moves on to more advanced content not addressed at the current grade level at a slow pace.
- Enrich: A student may work within the same topic as other students but his/her process and outcome differs.
- Increase Sophistication: A student explores a similar topic at a higher or more abstract level.
- Use Novelty: A student is exposed to completely different material not found in the regular curriculum.
- assign more work
- give free time when finished
- assign gifted learners to help struggling learners
- pull-out gifted learners
- give independent enrichment on the computer
To end the chapter, the authors asked another “Stop and Reflect” question that is a great reflection for all chapters thus far—one to really think about—“How is equity in the classroom different from teaching all children equitably?
We would love to hear your thoughts, so please feel free to leave a comment! Also, you will want to visit the other participating bloggers in the link up below.
Courtney will be here on Wednesday for a discussion of chapter 7, so come back and join us! I will see you next Sunday!
All the best for a wonderful week ahead!