Language Development in Mathematics Classrooms
James Brickwedde, Project for Elementary Mathematics
| Standards of Mathematical Practice (What Students Do): MP3: Construct viable arguments and critique the reasoning of others |
The following material summarizes new professional development materials found on the Minnesota STEM Teacher Center website. The material was developed with a grant from MDE & COMPASS. This is the third in a series of summary articles for MathBits.
Every teacher in a mathematics classroom is a language teacher. The question is, is the teacher conscious of that fact. Building a student’s voice to express the strategies and subsequent decision making choices, to justify an answer with evidence, and to “critique the reasoning of others” provides an entry to the community with whom one is engaging. This is an issue of access. Aiding a student in commanding the content language of mathematics is an integral part of building that voice, but it is not enough. One has to learn to communicate one’s own ideas, collaborate with others while solving problems, and to communicate findings appropriately to various audiences. All of these capabilities are language communication skills.
These skills are learned. As mathematics classroom educators, it is essential that intentionally developing these language skills are seen as much a part of the lesson planning as for the content itself.
Figure 1
Standards for Mathematical Practice ←→ Mathematics Teaching Practice
|
Standards for Mathematical Practices |
Eight Mathematics Teaching Practices |
| MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning |
1. Establish mathematical goals to focus learning 2. Implement tasks that promote reasoning and problem solving 3. Use and connect mathematical representations 4. Facilitate meaningful mathematical discourse 5. Pose purposeful questions 6. Build fluency from conceptual understanding 7. Support productive struggle in learning mathematics 8. Elicit and use student thinking |
Figure 1 lists the eight Standards of Mathematical Practice (What students do) and the eight Mathematics Teaching Practices (What teachers do). Minnesota’s 2022 draft mathematics academic standards builds on these two sets of dispositions and practices. In the November MathBits, a look at posing purposeful questions (5) to elicit and use student thinking (8) in order to facilitate meaningful mathematical discourse (4) was discussed. Extending that conversation here, and keeping in mind the various student and teacher practices, if one is to promote reasoning (MP2) by using and connecting through mathematical representations (MTP3), then language is needed to do so. If meaningful mathematical discourse (MTP4) is enacted by posing purposeful questions (MTP5) for the purpose of eliciting and using student thinking (MTP8), then language is needed to do so. If you are one of the many teachers exploring Building Thinking Classroom (Liljedahl, 2022) practices, the students working in small groups and the public sharing of ideas requires communication skills not only of oral language, but in intensely listening to ideas, processing and debating those ideas, and communicating those ideas visually through numerical, graphical, and text-based formats. These are language-rich classrooms.
The new professional development material on the Minnesota STEM Teacher Center website is divided into four clusters. Cluster 3 focuses on language development. A core feature of classrooms that utilize these practices is that you hear students describing, explaining, collaborating, and sharing. In other words, there is a lot of talking. For those conversations to be purposeful and productive, students have to develop a skill set allowing them to develop their own voice, have the capacity to actively listen to others, and to comprehend the perspective of another as that individual’s point of view is considered. As the instructional leader in the classroom, it requires developing those discourse practices and the community of practice in which students feel emotionally and intellectually safe in communicating ideas (Brickwedde, 2022). This is attained through repeated, strategic, iterative, and supported opportunities to articulate complex mathematical ideas, negotiate the meaning of those ideas with others as claims are justified with evidence, conjectures are made and explored, and ideas are constructively critiqued (Zwiers, et al., 2017).
Vygotsky states that thought is language and that mathematics is socially negotiated among one’s peers. Intentionally incorporating in one’s lesson plans the language functions one wants the students to focus on, therefore, becomes the essential bridge between thought and the community. Examples of language functions are explain, describe, justify with evidence, paraphrase, summarize, compare and contrast, etc. Planning for the type of grammatical syntax students may need to organize their thoughts such as proving sentence stems: “First I did… Next I did… ; I agree/disagree with ___ because… ; I chose to do ___ because I wanted to ___, etc. These are the tools by which students become increasingly articulate in their communication skills. Some students may understand the mathematics but lack the skills to formulate the language around which to explain and justify their reasoning. Assisting students with specific language skills allows the student to be clearer to themselves (expressive/reflective speech), and to their peers (descriptive speech). Their thinking becomes clearer, more robust as the precision of their language improves. From a teacher perspective, the quality of the formative assessment within the classroom is richer as one can more clearly understand students’ processing.
In many schools across the state, there are ESL teachers on staff. These colleagues are assets and allies for you to collaborate with to better understand the development of language skills among your students, whether or not you have any multilingual students on your rosters. This language-rich classroom is where the 2022 Minnesota draft mathematics academic standards are directing teachers to develop. Think of all students as needing to become multilingual in the mathematics learning environment. If such a learning environment is well integrated into one’s teaching practices, then when one has a multilingual student from another country, supporting that student becomes easier. The core practices are already in place. Only some additional supports may need to be added to the mix but the core practices are built for universal access.
References
Brickwedde, J. (2022). Instructional Practices: Building Student Voice and Active Listening Skills. Retrieved from Project for Elementary Mathematics: https://drive.google.com/file/d/10YvN5Vywbct8IHuvR60YGCklXzpa-ZvT/view?usp=sharing
Liljedahl, P. (2021). Building thinking Classrooms in Mathematics Grades K-12. Corwin: Thousand Oaks, CA.
Zwiers, J., Dieckmann, J., Rutherford-Quach, S., Daro, V., Skarin, R., Weiss, S., & Malamut, J. (2017). Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Retrieved from Stanford University, UL/SCALE website: https://ul.stanford.edu/sites/default/files/resource/2021-11/Principles%20for%20the%20Design%20of%20Mathematics%20Curricula_1.pdf