From Spatial-Temporal Learning to Academic Language

ST Math invites students to learn through spatial-temporal reasoning, which often by-passes language altogether as students develop mathematical schemas, making it highly accessible to students who are learning a new language, have challenges processing language, or any student who is learning new mathematical vocabulary.

ST Math games and Puzzle Talks provide a though-provoking and engaging foundation for discourse in a mathematics community–asking questions, sharing strategies, building on or critiquing other approaches, and moving from informal or situational understanding into formalized concepts that are more efficient and can be transferred to new contexts. As students get excited about ST Math games, it is natural for them to want to discuss what they notice, wonder, and would like to try–excellent opportunities to move them gradually toward using more academic language to express their ideas.

ST Math games and Puzzle Talks can be used either before students have learned any formal vocabulary for a concept as a creative introduction that makes new language acquisition meaningful or afterward to reinforce concepts and language in a new context.

Introducing New Vocabulary through ST Math

Students learn vocabulary more effectively when they have already built a schema for the concept, such as through playing ST Math and using their own language to make connections during Puzzle Talks or in small group/class discussions.

Encourage students to describe what they notice, wonder, and want to try in an ST Math game using their own informal language. After students have shared their thoughts to take ownership of the ideas and build a strong schema, introduce formal vocabulary for the concept as part of the discussion.
After introducing a vocabulary term, rephrase students’ questions and thoughts to use the new vocabulary term correctly. This provides students with a natural way to both hear and use the vocabulary in context.
Return to students when working on a later puzzle that uses the same vocabulary and ask questions about what strategies they are using and why. Encourage students to use academic vocabulary when responding.
After students have had the opportunity to use new vocabulary in the context of the game, use one or more of the approaches in the Building Academic Vocabulary section to deepen students’ understanding and support use over time.

Connecting Known Vocabulary through ST Math

Students can deepen and reinforce academic vocabulary when they transfer what they have already learned to the new context of ST Math games or Puzzle Talks.

When asking students about their strategies or observations, rephrase students’ responses using academic vocabulary (e.g., “Ah, so you partitioned the fraction into equal parts.”) or ask follow-up questions that model using the vocabulary in context (e.g., “How did you know how to partition the fraction?”).
Ask, “What does this remind you of? How is this similar to or different from other things that we’ve learned? What did we call this when we learned about it before?” Encourage students to explicitly transfer vocabulary from other contexts when describing what is happening in an ST Math game.
Use math routines such as the Labeling Strategy Planner or the Journal Pages “Today’s Accomplishments” or “Math Journal with JiJi” to support students in making connections between academic vocabulary and ST Math games.
After students have had the opportunity to use new vocabulary in the context of the game, use one or more of the approaches in the Building Academic Vocabulary section to deepen students’ understanding and support use over time.

Introducing Academic Vocabulary

For native speakers as well as students learning a new language, introducing vocabulary should be done purposefully and in a context that allows students to connect new vocabulary to an existing schema and continue to practice using it flexibly. Consider these approaches when introducing new vocabulary in an ST Math discussion or Puzzle Talk.

Routines for Introducing Vocabulary: Establish a clear routine for introducing new vocabulary. For example, have students describe a concept with their own words during a Puzzle Talk or while playing an ST Math game. Then, introduce the word by giving a student-friendly definition and connecting it to the visual model on the screen. Write the word on the board, model pronunciation, have students repeat the word out loud, and then prompt students to use the word to describe the next puzzle in a class discussion, partner share, or in writing. Follow up by having students add the word to an anchor chart, word wall, or vocabulary journal, as described in the Supporting Academic Vocabulary section that follows.
Pre-plan Vocabulary Introductions: Use the vocabulary list at the top of each Puzzle Talk to plan a sequence for introducing each new vocabulary term. For example, you may want to do the first puzzle with students using their own language, introduce one vocabulary word in the second puzzle, and introduce two more related vocabulary words in the third puzzle. Then, use the last two puzzles to support students in using the new vocabulary terms in context. See How can I use any game for a Puzzle Talk? to introduce vocabulary through discussion around any ST Math game.
Concrete and Visual Representations: Pair academic vocabulary with visual representation in ST Math games or other visual or concrete representations (e.g., fraction bars, number lines, place value charts, algebra tiles) and explicitly connect them to vocabulary. Support students in linking abstract concepts to visual and tactile experiences by describing and using vocabulary while playing ST Math games and transferring their learning to new contexts.
Provide Dual-Language Dictionaries: As students encounter new concepts in school, they may learn vocabulary in English that they have not yet learned in their home languages. Provide dual-language dictionaries online or in print to support students in learning and connecting vocabulary in both languages.
Academic vs. Non-Academic Meanings: Explicitly teach multiple meanings of academic terms that have a different meaning in everyday English (e.g., difference can mean the result of subtraction or how two things are dissimilar; table can mean a chart with rows and columns or a flat surface with legs; round can mean finding the nearest multiple of a power of ten or a curved surface). Use clear explanations, gestures, and visuals to demonstrate and compare each meaning.
Cross-Linguistic Connections: Make cross-linguistic connections clear. Highlight cognates (e.g., angle/el ángulo, circumference/la circunferencia in English and Spanish) and false cognates (e.g., a billion is 1,000,000,000 in English, but this number is called mil millón or a thousand million in Spanish, while billón means 1,000,000,000,000; in English large means big, but in Spanish largo means long). Facilitate discussions or provide free-writing opportunities where students explore similarities and differences between students’ home languages and English to deepen understanding of key ideas and support vocabulary acquisition.
Identify Language Roots: When introducing new vocabulary, support students in noticing Greek, Latin, and English prefixes, suffixes, and roots that help identify the meaning of the word and how it is used grammatically. Help students make connections to similar words, such as noticing that denominator has the root nomen (name, similar to nombre in Spanish), the suffix -ator (something doing an action), and the prefix de- (coming from, giving, down, or off), so the entire word means the thing that gives the name or tells the name of the size of the fractional parts.

Supporting Academic Vocabulary

ST Math game discourse and Puzzle Talks are best supported by ongoing classroom routines for making academic language accessible and supported using approaches such as the ones below.

Vocabulary Logs and Graphic Organizers: Support students in exploring, recording, and recalling vocabulary with Multilingual Vocabulary Tools. These tools support students in making connections between vocabulary terms across languages and exploring their meanings with definitions, models or drawings, examples, non-examples, and other memory aids.
Anchor Charts: Anchor charts are posters that students co-create with teachers with text and visual supports for content and vocabulary. At the beginning of each unit or major content area, begin an anchor chart and prompt students to collaboratively define key terms with images, examples, and connections between ideas as new vocabulary and content are introduced across the unit. Encourage students to reference them during Puzzle Talks or when discussing or writing about ST Math games.
Word Walls: Word walls (communal ward banks) use cards or papers to show academic vocabulary that students can draw on as they think, speak, and write. As each new vocabulary word is introduced, create a new word card with an appropriate illustration or definition to post on the wall, sorted alphabetically or by topic. Consider having students create word cards to show their co-ownership of the language and growing vocabulary.
Sentence Stems: Use Sentence Stems to support language learners in using vocabulary in sentences. See the Supporting Oral and Written Discourse section below for more information.
Vocabulary Games: Integrate vocabulary into games that support meaningful schema-building, such as the following:
- Use the Back to Screen Planner to challenge students to use academic vocabulary when describing an ST Math puzzle to a partner who cannot see the screen.
- Use the Labeling Strategy Planner to support students in labeling academic vocabulary in an ST Math game screen.
- Show students a screen from an ST Math game that students are already familiar with and challenge students to make a word web with as many related vocabulary words as they can, showing the connections between them.
- Show students a screen from an ST Math game that students are already familiar with and think of a vocabulary word without sharing it. Play 20 questions, where students get to ask 20 yes or no questions to help them guess the vocabulary word. Rotate so that a student thinks of the mystery word in the next round.
Spiral Vocabulary Use: When students re-encounter academic vocabulary that they’ve already learned, prompt students to recall how they’ve used the terms in the past and make explicit connections to how they’re used similarly or differently in a new context. Look for opportunities to have students speak or write with precise academic vocabulary as they encounter concepts in ST Math and the classroom that may occur at different points of the year. Consider using Puzzle Talks as a review later in the year to reinforce long-term memory of concepts and vocabulary.

Supporting Oral and Written Discourse

ST Math puzzles provide a rich and intriguing opportunity for oral and written discourse that builds students’ receptive and expressive language skills. Encourage collaborative problem solving and sharing strategies with planned supports for language learners, such as the ones below:

Facilitate Mathematical Discussions: Puzzle Talks are designed to support students in connecting their spatial-temporal reasoning with language in whole-class discussions. Use the Discourse Questions and Look Fors to support the transition from visual thinking to informal language to academic language by asking open-ended questions that invite students to share their thinking and then following up with questions that use increasingly specific academic vocabulary and language formats. Rephrase students’ responses to help students make connections between their own ideas and academic language.
- See How can I use any game for a Puzzle Talk? to extend this to any ST Math game.
- See the Facilitation Quick References guide from The Problem Solving Process page for discussion prompts that you can use to support mathematical discussions about any ST Math game or Puzzle Talk.
Sentence Stems: Provide sentence stems to support students in expressing their thinking with their own language and using increasingly specific academic vocabulary. Share the Sentence Stems chart from The Problem Solving Process with students to support any ST Math game or Puzzle Talk. When discussing a specific ST Math game, provide sentence stems that address content and vocabulary, such as “The quotient is _____” or “I divided the ______ by the _____ because. . .”. See the section on Guiding Students to Use Increasingly Sophisticated Academic Language below for ideas on scaffolding sentence stems.
Extend Writing and Speaking During Puzzle Talks: The Engagement Strategies chart from the ST Math Puzzle Talks page provides a set of short activities that encourage students to think, speak, and write about their ideas during Puzzle Talks or any discussion around ST Math games.
Paired Puzzling: Support comprehension through collaboration by having students work on an assigned ST Math game on both students’ devices at the same time. Encourage students to discuss what they notice, wonder, and want to try, then to explain the strategies or concepts that help them make sense of the puzzle. Encourage students to use their own language first, then transition to academic language as it is introduced or they become more familiar with the puzzle.
Turn and Talks: Structure frequent opportunities for students to talk about their thinking with a partner, even if students are working on different games. For example, have students pause in the middle of ST Math game play to share the puzzle that they are working on with a partner and explain how they knew what to do. At the end of an ST Math session, instruct students to share the most interesting thing that they learned that day, share one strategy that they thought was effective, or share a connection between an ST Math game and something they have learned in class. Encourage partners to ask clarifying questions or restate what they learned from their partner using academic language.
Journal Pages: The ST Math Journal Pages provide opportunities for students to share their thinking with writing and drawing, as appropriate by age or language acquisition level. Students are guided to reflect on content, effective mathematical strategies, ways that they approached problem solving, mistakes, vocabulary, and connections with learning from other classes, as well as making written notes as they move through the problem solving process.
Quick Writes: Support language development and check for understanding through quick writes or exit tickets at the end of a Puzzle Talk or when playing ST Math games. For example, if all students are working on the same assigned learning objective, write three key vocabulary words on the board and challenge students to use them while describing the strategies that they used in a recent ST Math puzzle. If students are working on different self-paced learning objectives, challenge them to use any three vocabulary words from a word wall or prior knowledge to describe the strategy they used in a recent puzzle.

Guiding Students to Use Increasingly Sophisticated Academic Language

Students with different levels of language proficiency benefit from different levels and types of support as their language skills grow. ST Math’s spatial-temporal games provide a rich space for exploring concepts without language, which students can build on as they apply increasingly sophisticated academic language during discussions or in writing. Consider these approaches to support students at different levels.

Scaffolded Sentence Stems: Provide scaffolded sentence stems that gradually increase in complexity:
- Pre-production learners: Read sentence frames out loud and have students only say the missing word or point to a visual cue or part of a model to complete the sentence.
- Beginning learners: Support familiarity with generalized vocabulary, such as “The answer is ___ because ___.”
- Intermediate learners: Provide sentence stems with embedded academic vocabulary to support using it in context, such as, “To find the area of the triangle, I started with a base of __ and a height of __, and then I _____.” Provide sequenced sentence stems that support connected and multistep explanations, such as “First, I ___, then I ___ to solve ___. This shows ___.”
- Advanced learners: Provide open-ended prompts that encourage detailed explanations with clear academic language and allow students to determine their own sentence structures. For example, “The expression can be simplified to . . . because . . . . I verified my results by . . . .”
Sportscasting: Sportscasting supports receptive language learning by describing what a student is doing play-by-play as they solve a problem, which is especially effective for pre-production and beginning language learners. For example, while a student is playing an ST Math game or demonstrating their strategy for the class, you might say, “You’re starting at 0 on the number line. You made one hop that was 3 units. You’re making 5 hops that are each 3 units to multiply. You’re clicking on the number 15 to show that 15 is the product. Now you’re clicking the green arrow to check your answer.”
Using Math as a Common Language: Encourage students to begin by recording their thoughts with numbers, models, expressions, or equations, then support them in describing their steps through sentence stems, vocabulary banks, and other strategies.
Co-Explaining: Partner with a student or have two students work together to describe a mathematical concept or approach, such as explaining the feedback animation in an ST Math game or how to model the feedback from a game with a Game Mat or Math Mat. Adjust the level of support provided by scaffolded sentence stems and the use of vocabulary banks to allow the language learner opportunities to show what they know while getting just-in-time support for areas that are still a growing edge.
Translanguaging and Translating: Translanguaging encourages and celebrates students as they use their full linguistic knowledge to learn and express themselves. Beginning language learners might use an online translation tool to speak or write an explanation in their home language and then read the translated output to themselves to build language knowledge or out loud to others to participate in classroom discourse. Intermediate language learners might jot down notes and solve problems in a home language and then translate their final steps into a target language with the support of a dual-language dictionary, word wall, or peer. Advanced learners can move fluidly between languages, choosing the one that works best for them in a given situation or with different peers.

Supporting Word Problems

Word problems appear in some Puzzle Talks and ST Math games, or can be used to extend students’ learning from ST Math games. When students address word problems, consider these strategies:

Introduce Contextual Vocabulary: Introduce contextual vocabulary (e.g., muffins, checking account, electric bill, etc.) through images, examples, and gestures. You may want to prepare images from a web search in advance. Invite students to share relevant experiences with the context with a partner to make connections to prior knowledge.
Slow Reveal Problems: Cover some words or numbers in a word problem to do a “slow reveal”, helping students notice how much they can understand without knowing all of the words. For example, in the problem “Mia had __ _____. She shared the _____ equally between __ friends. How many _____ did each friend get?” students should recognize the division context, even if they don’t know what objects are being divided or any of the numbers involved.
Paired Reading and Sense-Making: Pair students to read and annotate problems together in English or another shared language. Encourage students to monitor their comprehension and then discuss the strategies they used to make sense of the language (e.g., underline key information, visualize the scenario, rephrase the question, look up an unknown word), determine which operations to use, or try other approaches if they get stuck (e.g., reread a confusing section in context, act out the scenario, decide not to worry about a new word if they can solve the problem anyway).
Paired Solving and Writing: Pair students to solve word problems and answer in complete sentences using English or a shared home language, including translating between them. Encourage students to first focus on mathematical ideas and incorporating academic vocabulary, then do a second pass through their writing to check for spelling and grammar as time allows.

Dive Deeper:
ST Math, Emergent Bilingual Learners, and the English Language Proficiency Standards (ELPS)