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Going Beyond the Numbers

How Teaching Students to Think Critically Helps English Learners Improve in Math 

Sandy Del Mundo and Melissa Herrera sit next to each other in a cubicle.

Sandy del Mundo (left) and Melissa Herrera (right) support MUSD's English Language program.

Math is more than just numbers and formulas. It is a way of thinking, a way of making sense of the world, and a way of solving problems. But for many students, especially those who are learning English as a second language, math can be intimidating and frustrating. In Manteca Unified, our direction is clear: How can we help students develop important math skills?

One method MUSD is focusing on this year is Thinking Strategies, a set of tools that help students engage with math concepts and tasks in meaningful ways. Thinking Strategies are not specific to math, as they can be applied to any subject or situation that requires reasoning and problem-solving. They are based on the idea that learning is an active process where students construct their own understanding by drawing on their background knowledge, asking questions, making inferences, visualizing and representing, determining importance, synthesizing, and monitoring for meaning.

Thinking Strategies help English learners improve their math skills by engaging them in meaningful tasks that provide them with multiple ways to access and demonstrate their learning. While these strategies give students the tools to expand their perspectives, they also create opportunities for interaction and collaboration and allow English learners to develop their academic vocabulary.

“Thinking Strategies get kids thinking about how they think,” shared Melissa Herrera, one of Manteca Unified’s Teachers on Special Assignment (TOSA) who specializes in the English Language program. “For English learners, these strategies are a vehicle to help students feel more confident in using language.” 

English learners spend a minimum of 30 minutes of protected time a day in class to practice language acquisition aligned to the ELD standards, but that’s not to say extra support isn’t needed when it comes to the curriculum, including math. This is where Thinking Strategies can really benefit instruction and make a positive difference.

While English learners are very capable of understanding math concepts, they may be unfamiliar with certain academic terms. Thinking Strategies can help order students’ thoughts and allow them to make connections between their primary language and academic language in English to reach a place of understanding. This is often achieved by adding visual communication tools, such as color coding, pictures, and charts.

“Thinking Strategies also give teachers insight about how students think and approach problems, which helps gauge if students are understanding what they are learning, or if they need additional support to achieve a lesson or reach a standard,” stated Sandy del Mundo, another TOSA focused on the English Language program in MUSD.

two students facing the board, working on a math problem.


Since Thinking Strategies are an important instructional tool for educators, this year, Melissa and Sandy are focused on helping teachers provide thorough, effective instruction for students. Both are working with teachers to embed scaffolds supporting thinking strategies to amplify language for English learners.  

During this process, the two TOSAs work to ensure that teachers know they’re here to help.

“We don’t want teachers to feel overwhelmed or that we’re asking them to implement something new. We want to help support the work they are already doing,” Sandy shared.

A critical aspect of this process is making sure teachers feel heard. “I often ask teachers, ‘What’s going on? and ‘How do you feel?’ because it’s important for them to feel validated in their experiences. We want to encourage them, not discourage them,” Melissa stated.

Thinking Strategies

Draw on Background Knowledge

“This is just like …”
“This reminds me of …”
“I know that …”

Ask Questions

“How …”
“What …”
“Why …”


Making logical guesses and predictions based on the information given and background knowledge.

“I’m thinking that …”
“I predict …”
“I am guessing that …”

Determine Importance

Identifying the main idea and the key details and filtering out the irrelevant or distracting information.

“I think this is really important.”
“This is essential … This is extra …”
“The big ideas are …”

Monitor for Meaning

Checking the solution for accuracy and reasonableness by using estimation, calculation, and logic.

“I’m confused here …”
“I understand this …”
“This doesn’t make sense …”

Visualize and Represent

Creating mental images to help understand and organize one’s thinking.

“In my mind, I can see …” 
“I would show this by …”
“Another way to show this is …”


Combining the information given and background knowledge to create a greater sense of understanding.

“At first I thought … But now I am thinking …”
“Now I understand that …”
“My thoughts have really changed by …”
  • Thinking Strategies
  • math