Educators implementing balanced literacy practices are noticing the difference. Explicit modeling of strategy is empowering students to apply approaches in novel situations. Thinking aloud is revealing previously cloaked cognitive processes. Accountable talk is raising the rigor of academic conversation and collaboration. Independent practice is leading to authentic application and differentiated support for all learners.
Practitioners are wondering whether balanced literacy techniques can also grow strategic math thinkers, particularly in relation to solving word problems. Transferring good teaching practices from balanced literacy to mathematics instruction will support your students, whether they are exploring the number line in Kindergarten or solving for a variable in eighth grade algebra.
Think Aloud about Word Problems and Encourage Metacognition
Thinking aloud and modeling “in the head” strategies helps our students understand how proficient readers and writers persist, problem-solve, and persevere when facing challenging texts or tasks. Thinking aloud about our math thinking will provide a similar anchor for budding mathematicians in our classrooms. In Mathematical Practices for Deep Understanding (Ed Leadership, 2014) Dean and Brookhart suggest, “Students must have clear “look-fors” to monitor the quality of their work and thinking.” Provide your students with explicit instruction as you tackle word problems aloud during your math lesson. Integrate your math thinking with your “literacy” thinking to illustrate ways in which you transfer your reading skills through a math lens. For example, think aloud as you annotate a word problem. Use explicit language to make your thinking visible such as, “Hmm…this word is tricky. I don’t recognize this word but I can use the words around it to help me find it’s meaning. Watch me as I…”
Remind students to use metacognition, or “thinking about your thinking,” by modeling strategies including the following:
- Pause and reflect during reading of word problems
- Actively consider possible strategies such as questioning the problem (e.g. What is the author asking me to figure out in this problem?), visualizing components of the problem narrative (e.g. making a mental movie about problem components), and determining importance (e.g. annotating critical information in the problem)
- Monitor for lost meaning while tackling the problem
As you model, keep in mind that readers don’t typically engage with a text by first asking, “What kind of book is this?” Rather, proficient readers often begin by interacting with the text as they read the back cover, flip through pages, dive into the first few pages, and connect schema with pictures on the cover. Dean and Brookhart remind us that, “Students who make sense of word problems don’t start by asking, “What kind of problem is this? They start by trying to figure out what the problem means.”
Model the ways in which you make meaning from word problems with questions that include the following:
- What is this problem asking?
- What information is given?
- What information is missing that I need to find?
- What math strategies can I use to find that information?
- What words seem important in the problem?
- What diagrams or tables can I create to help me keep track of the information in the problem?
- What do I know that can help me tackle this problem?
- What mathematical symbols can I infer from the language in the problem (e.g. some more apples = addition)?
As you model, you might annotate places in the word problem that illuminate meaning or cause confusion. Remember to continually anchor your thinking to the purpose of the problem. For example, you might say, “Ok, I remember the problem was asking…I just found this information in the problem that might help me to do that. I think I’ll circle this information.”
Presenting the Problem First
In her article Introduce Word Problems to Students Sooner, Studies Say (Education Week, 2014), Sarah Sparks cites studies suggesting, “that word problems might be easier and more beneficial for students when presented at the beginning, not the end, of a mathematics lesson.” In a middle and high school study conducted by University of Wisconsin-Madison professor Mitchell Nathan and colleagues, “students were randomly assigned to solve different versions of the same problem: a symbolic equation, a story problem using that equation, or a non-narrative word problem of the equation.” Findings revealed students were more likely to tackle word problems than equations. Additionally, Nathan’s study demonstrated that, “Working through narrative problems also made students feel more empowered to explore different methods of solving a problem, rather than following a single sample process.”
In the following video, Jen Saul, grade three teacher, presents the problem at the beginning of the lesson and elicits student “empathy” by requesting student help in tackling the problem. Saul uses a “think sheet” with visual models that cue strategic thinking. These models include a two-column table, shapes that encourage diagramming, and a box with question prompts like, “What do you know?” and “What do you need to know?”
Starting with the problem in Nathan’s study prompted some students to use textual clues from the word problem to “guess and test” variables in an equation while others attempted to “unwind a story problem” to logically order operations in the problem. In either case, students used narrative structure and story content to deduce mathematical processes when presented with the provocation at the onset of the lesson.
Create a Culture of Risk-Taking, Stamina, and Communication
Dean and Brookhart remind us to give students time to read the problem and consider how they might tackle the problem, as well as critical time for “each learner to share with a partner what they think this part of the problem is asking and their plan for solving it.” Saul also emphasizes the importance of classroom culture in her video. Parallel to balanced literacy instruction, students in math class need time to tackle problems independently, with teacher coaching and with peer collaboration. Use familiar accountable talk routines and protocol to foster rich math talk in your classroom. Before engaging in solving the problem, pairs or groups can talk about schema, or background knowledge, they can potentially apply to the problem. During problem-solving, student talk sounds like clarifying, sharing important information gathered from the problem, and thinking aloud through their proposed problem-solving steps (metacognition). After problem-solving, student talk may include justifying use of particular approaches, reflecting on problem-solving challenges, preferences, and outcomes, and refinement of strategies based on peer feedback.
Model accountable talk in math just as you would for literacy work. Prompt effective talk in guided practice or as you listen in on small group conversation with questions such as the following:
- Does anyone have evidence they can use to support _____’s idea/solution?
- Is there another point of view?
- Can you explain your thinking?
- Let’s stay with ____’s idea. Who can say more? Does anyone have a question about that strategy/solution?
- How does that compare to your thinking?
- We have two strategies on the table already. Which strategy is resonating with you? Why?
Create an anchor chart to support math talk in pairs or groups with possible sentence starters.
- I agree with ____ because…
- What makes you say/think that?
- That makes me think…
- Can you show me how you…
- My strategy is similar to ____’s in that…
- I don’t understand. Can you say more about that?
- I’m also thinking…
- I’m confused. Can you help me understand what you’re thinking?
Educators implementing balanced literacy recognize the importance of formative assessment. This is equally critical in mathematics instruction. Dean and Brookhart assert that formative evidence “comes from three sources: watching students work, talking with students about their process, and observing the final product. “ The authors encourage a feedback that is descriptive and focused on the process of problem solving more importantly than the product. Feedback can be delivered during conferring conversations, sticky note comments on a think sheet or math journal, or in the context of small group conversation. Include next steps students can pursue in your feedback during formative assessment. Next steps may include discerning between more and less effective approaches to a problem, refinement of a strategy, or application of a new strategy you’ve offered. As in balanced literacy, it is critical to “structure classes so that students have immediate opportunities to take those next steps.” Time for independent problem solving, group investigations, guided math, peer partnerships, and conferences will ensure students have the opportunity to put your feedback into practice.
Keep in mind that the formative assessment cycle is a process by which data informs your instructional planning. Use a wide variety of formative tools to collect qualitative and quantitative data including Math Notebooks, Exit Slips, 3-2-1 worksheets (3 questions I have, 2 ideas I need to talk more about, 1 concept I’m feeling confused about), math graffiti boards (chart paper or board space where students can post sticky notes with questions, comments, or confusions, as they occur during problem solving), conferring notes, data recorded during group work/instruction, and standardized assessments for math fluency, conceptual application, and synthesis. Don’t forget to engage students in the assessment process. Their self-reflections and self-assessments will help them become confident mathematical thinkers.
Dean, C., & Brookhart, S. (2014, January 1). Mathematical Practices for Deep Understanding. Retrieved from http://www.ascd.org/publications/educational-leadership/dec13/vol71/num04/Mathematical-Practices-for-Deep-Understanding.aspx
Persistence in Problem Solving. (n.d.). Retrieved November 23, 2014, from https://www.teachingchannel.org/videos/problem-solving-math#
Sparks, S. (2014, November 1). Introduce Word Problems to Students Sooner, Studies Say. Retrieved from http://www.edweek.org/ew/articles/2014/11/19/13mathwords.h34.html?cmp=ENL-EU-NEWS1