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Phonological awareness is the ability to recognize and manipulate the spoken parts of sentences and words. Examples include being able to identify words that rhyme, recognizing alliteration, segmenting a sentence into words, identifying the syllables in a word, and blending and segmenting onset-rimes. The most sophisticated — and last to develop — is called phonemic awareness. (Phonological and phonemic awareness: Introduction 2022)

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https://www.youtube.com/watch?v=kJMsWoVeBjk&t=554s

Phonics - a method of teaching people to read by correlating sounds with letters or groups of letters in an alphabetic writing system. (Oxford)

"Phonics instruction teaches the relationships between the letters of written language and the sounds of spoken language. To read, children need to understand the alphabetic principle — the idea that letters represent the sounds of spoken language. Decoding is when we use letter-sound relationships to translate a printed word into speech." (Phonics and decoding 2023)

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Mastering Short Vowels and Reading Whole Words with Calista, First Grader

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"Fluency is the ability to read a text accurately, quickly, and with expression. Fluent reading builds stamina for reading lengthy or complex texts. Reading fluency serves as a bridge between word recognition and comprehension." (Fluency 2023)

Mathematics definition:
"Mathematical fluency is the ability to quickly and accurately recall mathematical facts and concepts. It’s made up of 5 key parts – accuracy, flexibility and appropriate response, efficiency, automaticity, and number sense." (Best, 2021)

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"Comprehension is the understanding and interpretation of what is read. To be able to accurately understand written material, children need to be able to (1) decode what they read; (2) make connections between what they read and what they already know; and (3) think deeply about what they have read." (Comprehension 2015)

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"Vocabulary refers to the words we must understand to communicate effectively."

"Educators often consider four types of vocabulary: listening, speaking, reading, and writing."
Listening - refers to the words we need to know to understand what we hear
Speaking - consists of the words we use when we speak
Reading - refers to the words we need to know to understand what we read
Writing - consists of the words we use in writing

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More resources: Vocabulary: self-paced course Target the Problem: Vocabulary Vocabulary Apps Topics A-Z: Vocabulary Vocabulary refers to the words we must understand to communicate effectively. Educators often consider four types of vocabulary: listening, speaking, reading, and writing. Listening vocabulary refers to the words we need to know to understand what we hear.

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Writing - the activity or skill of marking coherent words on paper and composing text (Oxford dictionary)

"Writing is a complex process that requires a wide range of skills — a strong vocabulary; an understanding of genre, text structure, and voice; basic mechanical skills (grammar and punctuation); organizational skills; and higher order thinking." (Writing 2023)

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More resources: Writing and Spelling (PBS Launching Young Readers series) Growing Writers (PBS Launching Young Readers series) Looking at Writing Writing: Course Module Writing Apps Topics A-Z: Writing A child's writing development parallels the child's development as a reader.

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Regional Educational Laboratory Southeast, R. E. L. S. (2023, January 16). What does 20 years of research say about teaching language and literacy in preschool?. Reading Rockets. https://www.readingrockets.org/article/what-does-20-years-research-say-about-teaching-language-and-literacy-preschool

Oral language. Reading Rockets. (2023, March 15). https://www.readingrockets.org/teaching/reading-basics/oral-language

Oral language impairments and dyslexia. International Dyslexia Association. (2020, April 1). https://dyslexiaida.org/oral-language-impairments-and-dyslexia-2/

Phonological and phonemic awareness: Introduction. Reading Rockets. (2022, October 3). https://www.readingrockets.org/teaching/reading101-course/modules/phonological-and-phonemic-awareness-introduction

Singh, M. (2022, September 24). How does math help in building phonics skills?. Number Dyslexia. https://numberdyslexia.com/math-and-phonics/

Phonics and decoding. Reading Rockets. (2023b, January 17). https://www.readingrockets.org/teaching/reading-basics/phonics

National Reading Panel. (2017, August 12). Phonics instruction. Reading Rockets. https://www.readingrockets.org/article/phonics-instruction

Bardell, T., & Archibald, L. (2023, April 19). Oral Language Skills and Learning Disabilities. LD@school. https://www.ldatschool.ca/oral-language-skills/

Print awareness. Reading Rockets. (2023c, January 17). https://www.readingrockets.org/teaching/reading-basics/printawareness

Fluency. Reading Rockets. (2023a, January 17). https://www.readingrockets.org/teaching/reading-basics/fluency

Best, J. (2021, April 6). Here’s why mathematical fluency is critical for problem-solving and reasoning. 3P Learning. https://www.3plearning.com/blog/mathematical-fluency-problem-solving-reasoning/#:~:text=Mathematical%20fluency%20is%20the%20ability,%2C%20automaticity%2C%20and%20number%20sense.

NCTM. (n.d.). Access and Equity in Mathematics Education. National Council of Teachers of Mathematics. https://www.nctm.org/Standards-and-Positions/Position-Statements/Access-and-Equity-in-Mathematics-Education/

Comprehension. Reading Rockets. (2015, March 23). https://www.readingrockets.org/helping/target/comprehension#:~:text=Comprehension%20is%20the%20understanding%20and,about%20what%20they%20have%20read.

Comprehension for English and maths? taking a cross-curricular approach. Oxford Education Blog. (2018, October 9). https://educationblog.oup.com/primary/comprehension-for-english-and-maths#:~:text=It%20is%20not%20only%20about,also%20crucial%20to%20English%20success.

Reading comprehension. Reading Rockets. (2023, January 17). https://www.readingrockets.org/teaching/reading-basics/comprehension

National Council of Teachers of Mathematics. (n.d.). Supporting Each and Every Student: Equity and Diversity. National Council of Teachers of Mathematics. https://www.nctm.org/conferences-and-professional-development/Tips-for-Teachers/Tips-on-Supporting-All-Students_-Equity-and-Diversity/

Reading Rockets. (2023b, January 17). Vocabulary. Reading Rockets. https://www.readingrockets.org/teaching/reading-basics/vocabulary

Writing. Reading Rockets. (2023c, January 17). https://www.readingrockets.org/teaching/reading-basics/writing

Franklin, & Marshall. (1994). Writing in Mathematics. Lancaster; fandm.edu.

What is academic writing?: DOS and don’ts for students. Scribbr. (n.d.). https://www.scribbr.com/category/academic-writing/#:~:text=Academic%20writing%20is%20a%20formal,and%20dissertation%20in%20academic%20style.

American Psychological Association. (2021). Inclusive language guidelines. https://www.apa.org/about/apa/equitydiversity-inclusion/language-guidelines.pdf

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Oral language encompasses both speaking and listening. Oral language skills include learning how spoken words sound, what words and sentences mean, and how to communicate ideas. Nurturing oral language skills provides a strong foundation for learning to read. (Oral language 2023)

Deeper definition:
Oral language refers to the knowledge and skills that we use to produce and understand spoken language. Language knowledge and skills also serve as the foundation for learning to read and write. Oral language is composed of five main components:

Phonology (understanding and use of the speech sounds in words)

Morphology (understanding and use of meaningful word parts, e.g., pre, un, ion)

Vocabulary or Semantics (understanding and use of the meaning of words)

Syntax (understanding and use of the grammatical aspects of language)

Pragmatics (understanding and use of language in various contexts) (Oral language impairments and dyslexia 2020)

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Oral language can be applied to students' learning in multiple ways. One way can be interactive reading. By asking students to rephrase a math problem or relate it to real life, students can gain understanding and recognition with oral language. It is through oral language that we can help students to gain a deeper understanding of mathematics by asking questions, such as why we do things, or why it works the way it does.
Another way oral language can be applied and developed is through small group activities. "When teaching language, students perform better when the intervention occurs in one- on-one or small group settings." (What does 20 years of research say about teaching language and literacy in preschool? 2023). Small group activities give students the opportunity to practice their oral language skills with one another, and possibly even the teacher.

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The REL Southeast research team summarized 20 years of research to identify instructional practices that best support the language and literacy development of preschool students. The systematic review included 109 rigorous studies that evaluated 132 language and literacy interventions. The review reported the overall impacts on students' language and literacy performance before entering kindergarten.

Supporting language development in preschool

Language is the foundation of thinking and learning. It is the ability to comprehend or use spoken language, which can include vocabulary, listening comprehension, syntax, or narrative understanding and production. Almost all interventions reviewed in the report included some language related instructional activities and some even taught language exclusively. The report identifies some effective instructional strategies and common misunderstandings when supporting preschoolers' language development.

Interactive book reading

Most of the interventions that taught language included interactive book reading as part of the instructional activities. In general, interactive book reading is an effective way to teach language. Specifically, evidence shows that asking questions before, during, and after interactive book reading can enhance the impact on language performance.

While reading a story, teachers may provide opportunities for students to find the main idea, connect text to students' life experiences, draw inferences beyond the text, make predictions, recall the story, or retell the story. Teachers may also introduce new vocabulary by labeling or identifying, defining, using word maps to generate synonyms and antonyms, or by providing examples and non-examples.

Small group activities support language development

One way to increase interactive instructional opportunities in your classroom is to carry out small group activities. When teaching language, students perform better when the intervention occurs in one- on-one or small group settings. Small groups allow students to receive more intensive instruction and allow teachers to have a more precise evaluation of student performance. Among interventions that taught language exclusively, the research team explored the impact of varying group size. Specifically, the review found that language-focused instruction had greater impact in groups smaller than six students than those occurred in whole group settings.

Is teaching language enough to prepare preschoolers for reading and writing?

Researchers have been putting efforts into answering this question. Evidence shows that using programs that solely teach language as primary curriculum does NOT produce the same impact on language performance as delivering language-focused instructional practices (such as interactive book reading) as part of the daily classroom routine. In fact, we found that teaching language exclusively is NOT likely to improve student performance in phonological awareness, print knowledge, decoding, or writing.

What else can be done to teach language effectively?

When talking with students, teachers can support expressive language development by modeling, extending, recasting, asking open-ended questions, or playing interactive games. An example of extending students' language is to repeat what a student says, and then add a few more words to extend the sentence. A recast is used to correct a student's incorrect phrase by rephrasing the sentence. For example, a student might say, "Him need juice." The teacher could respond with, "Does he need juice?"

For more information, please go to the other resources section for other strategies to promote language development in your classroom.

Supporting phonological awareness development in preschool

Phonological awareness involves being able to recognize and manipulate the sounds within spoken words. Research has shown that phonological awareness is fundamental for understanding the alphabetic principle and reading success. More than half of the interventions included in the report taught phonological awareness and the results demonstrated that students had better phonological awareness outcomes than those who did not receive the interventions.

Does phonological awareness have to be taught to be learned?

A small number of studies reviewed in the report evaluated the impacts on phonological awareness without teaching it. Some of these interventions included teaching letter names, letter sounds, or letter writing, but did not teach phonological awareness. The results showed that students are NOT likely to develop phonological awareness without being taught.

More importantly, the evidence further reveals that teaching phonological awareness and print knowledge not only benefited the development of them both but also improved decoding and early writing, even when neither of the latter skills were taught.

What are effective strategies to teach phonological awareness?

We found that interventions including a combination of exercises such as identification, matching, blending, counting, segmentation, or production can improve student performance. In addition to formal instructional practices in classroom, teachers can also embed these activities in the daily routine, such as during transitions, because phonological awareness activities can be done without using any print materials.

To identify a sound in a word, teachers may ask students to identify the initial phoneme* or rime unit in an orally presented word or in a word depicted in a picture. A matching task is when students match or sort words that share a common sound or rime. Students may also practice blending sounds into words or segmenting words into sounds. An example of production is asking the student to say the word that remains when "cil" is removed from "pencil."

For more information, please go to the other resources section for other strategies to promote phonological awareness in your classroom.

Supporting print knowledge development in preschool

Print knowledge is another building block in preparing students to become good readers and writers. More than half of the interventions included in the report taught print knowledge. Specifically, most taught letter names or sounds, and some taught concepts about print. It is worth noting that no intervention taught print knowledge exclusively. Print knowledge instruction frequently co-occurred with language and/or phonological awareness instruction.

Does order matter when teaching letter names and sounds?

Most students enter preschool having some knowledge of the alphabet. Regardless, teachers should still plan to teach all 26 letter names and their sounds. Of the studies included in the report, only a few examined teaching letter names/sounds sequentially, and little evidence supports one instructional order over another. In fact, teaching either letter name or letter sounds or both, all produce similar improvement in letter knowledge.

Is teaching letter names and letter sounds enough to prepare preschoolers for reading and writing?

Of all the interventions that taught print knowledge, some did not teach phonological awareness. We compared the impacts of these interventions with those that taught both. The results showed that interventions that taught both print knowledge and phonological awareness improved print knowledge performance, while interventions that taught print knowledge without teaching phonological awareness did NOT. Teachers can introduce letter names and sounds while also providing phonological awareness activities. There is no need to delay teaching print knowledge until after phonological awareness instruction or vice-versa.

What are other effective strategies to teach print knowledge?

Another component of print knowledge is concepts about print which includes the understanding that print carries meaning, and how a book "works." Some interventions introduced concepts about print by using print referencing during shared book reading. Teachers may direct students' attention to print by explicitly commenting on, asking questions about, pointing to, and tracking text that is being read.

For more information, please go to the other resources section for other strategies to promote print knowledge in your classroom.

Supporting decoding development in preschool

Decoding is the ability to understand letter-sound correspondence and to decipher new words by sounding them out. To determine the impact of different decoding focused instructional components, an intervention was identified as teaching decoding when it focused on manipulating sounds within printed words or translating a word from print to speech sounds. When these tasks were taught without printed words present, the interventions were identified as teaching phonological awareness instead of decoding.

Is it too early to teach decoding in preschool?

In this report, only a few interventions taught decoding and most included some phonological awareness or print knowledge instructional components. That being said, we found an overall positive impact on decoding, especially when phonological awareness and/or print knowledge were also taught. It is worth noting that the positive impact on decoding occurred even when only phonological awareness and print knowledge were taught. Teachers of this age group are encouraged to devote most of their attention to phonological awareness and print knowledge instruction which can lead to improved performance in decoding. More research is needed to explore the benefits of decoding instruction in preschool, and on how to best differentiate instruction for children with different levels ofphonological awareness and print knowledge.

What are other effective strategies to teach decoding?

Teachers may emphasize the relationship between the individual sounds in our spoken language and the letter we use to represent them in our written language. Learning how the 26 letters are used to represent the roughly 44 sounds in our spoken language allows students to unlock the code of our written language.

For more information, please go to the other resources section for other strategies to promote decoding in your classroom.

Supporting early writing development in preschool

Early writing is supportive of students' later literacy development. Preschoolers might start exploring writing with drawing, marking, or scribbling letter-like shapes. In addition, early writing also involves the understanding of general conventions such as English print going from left to right on a page, and how written language works (for example, speech can be represented by individual sounds, which can be written down using letters). Preschoolers' exploration with writing can demonstrate their knowledge of the English writing system.

Is it too early to teach writing in preschool?

In this report, most interventions that taught writing included some phonological awareness or print knowledge instructional components. Some studies evaluated the impact on writing even when the intervention did not teach writing. The evidence shows that teaching writing solely is not likely to improve writing performance. However, when interventions also included phonological awareness and print knowledge, we found a positive impact on writing even when writing was not taught. Teachers are encouraged to include writing in their overall instructional program, while also emphasizing language, phonological awareness, and print knowledge.

What else can be done to support preschoolers' writing development?

Writing time is considered an important activity in many preschool classrooms. Yet, it might be challenging to offer explicit writing instruction when your students have diverse experiences in writing. Besides playing with sounds in the words and introducing letters, teachers may demonstrate writing those taught letters or words, and encourage students to copy, trace, or even spell them when teachers see fit. Inviting students to write their names is another way to foster early writing skills. Writing instruction that address composition can help students make the connection between oral language and written language.

For more information, please go to the other resources section for other strategies to promote early writing in your classroom.

Other resources

Language

Phonological Awareness

Print Knowledge

Decoding

Early Writing

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What Does 20 Years of Research Say About Teaching Language and Literacy in Preschool?

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Children entering kindergarten vary greatly in their language and literacy skills. Therefore, up-to-date information about evidence-based practices is essential for early childhood educators as they support preschool children's language and literacy development. This comprehensive study identified interventions that improved students' performance in six language and literacy domains- language, phonological awareness, print knowledge, decoding, early writing, and general literacy.

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Oral language is important in a mathematics classroom for multiple reasons. Since oral language is used to communicate thoughts and ideas, its use in mathematics is varied. We need oral language to convey what the symbols mean, what the numbers mean, and what is being asked to do in a particular problem. It is through speaking and listening that we, as teachers, explain the use of mathematics to students and how to understand what is being asked.

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Application of phonological awareness in a mathematics classroom can look like a lot of things. For one, it can look like enunciating specific words so that students understand that there is a difference between one word and another word that may sound similar. For another, it can look like pointing out the prefix of words to better understand what the word means and how to recognize it in future scenarios. And, for yet another, it can look like breaking down a word problem into smaller pieces to get a better understanding of the information that is given and what we should do with the information. These are only a few examples of application of phonological awareness in mathematics, and there are endless examples that get applied daily in a math classroom.

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When it comes to oral language, not all people learn the same way. Although most children develop a knack for recognizing sounds and word patterns from a very young age, some people might have disorders, such as dyslexia, preventing them from being able to recognize and recall specific sounds.

"Children with dyslexia most often have the following problems with the phonological component of language:

Phonological awareness (explicit awareness of the sounds of language)

Phonological memory (memory for the speech sounds in pronunciations of labels (e.g., letter names), parts of words, or entire words)

Phonological retrieval (word and name retrieval)

Phonological production (pronunciation of multisyllabic and phonologically complex words, e.g., aluminum, specific)" (Oral language impairments and dyslexia 2020)

Possible solutions to teaching students with DLD (developmental language disorder) are:

Consult with a speech-language pathologist

Teach using the acronym SMART (S - slow down, M - [E]mphasize, A - add visuals, R - repeat instructions, T - time to respond)

Increase awareness of DLD (Bardell & Archibald, 2023)

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"Mathematical skills and abilities shape how a person associates language and phonics. Two main reasons are there that contribute to this particular trait. Mathematics is a subject that involves learning both numbers and words. So, when learners read a mathematical problem, they develop phonological awareness. Secondly, both math and language involve the use of memory. Language develops phonological memory, and math develops numerical memory. Together, a number-word learning process is initiated... Thus, math skills help improve phonic skills by improving phonological awareness." (Singh, 2022)

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Paying special attention to phonological awareness and all of the categories that fall under this umbrella term will help students of all types, whether they are English Language Learners, have dyslexia, or have any other sort of characteristic that might put a strain on the learning of mathematics. To be sure to reach all types of students, we should use the Universal Design for Learning (UDL). This includes using multiple means of representation, multiple means of engagement, and multiple means of action and expression.

https://www.youtube.com/watch?v=bDvKnY0g6e4

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Application of phonics in a math classroom will look a lot like the application of phonological awareness. In mathematics, we must be careful to enunciate when teaching brand new concepts, making sure to explicitly say the new word clearly and definitively. One way to apply phonics is to teach using analogy phonics and relate words using analogies, if possible. This means recognizing the rime segment in a word is familiar and relating it to another known word. Other methods can be used, too, such as analytic phonics, embedded phonics, phonics through spelling, and synthetic phonics. (Phonics Instruction 2017)  No matter which method is chosen, it is important for students to understand that the language of math is a very precise language.

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In a mathematics classroom, print awareness is important because it "is the understanding that print carries meaning, that books contain letters and words. Print awareness also includes an understanding of what books are used for and how a book "works" — how to turn pages, how to find the top and bottom of a page, and how to identify the title and the front and back covers." (Print awareness 2023)
Students need to be aware that everything in a mathematics classroom has meaning and they must be taught that meaning. Every symbol has a purpose, every word in a problem has a purpose, and math textbooks can be read to learn in addition to listening to the teacher.

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Developmental Language Disorder (DLD) is just one reason students may need additional support in a mathematics classroom. A way to support these students is by teaching using the S.M.A.R.T. acronym, which will ultimately benefit all students, regardless of disorders or language spoken.

S - Slow down the rate of speech
M - (E)mphasize key words during instruction
A - Add visuals such as pictures or gestures
R - Repeating instructions two or three times has been shown to be beneficial for students with DLD
T - Time to respond. We must give students time to process and also to craft a response

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3 ways to enhance fluency in a mathematics classroom are:

1. Practice repetition using games. Other benefits to games are:

They encourage thinking about mathematics on a strategic level

They need less teacher input and encourage autonomous learning

They build students computational fluency

They connect the classroom environment to the home learning environment

2. Daily mathematics fluency activities

Mathematics skills become strong when they’re done regularly. After a concept has been introduced, you should look to have activities planned to cement students’ knowledge until you’re confident they can work on it or use it independently.

3. Give students time to discover

Plan lessons that allow students time to discover number patterns, structures, and concepts and test them out in different situations to see if what they discovered works. This builds autonomy and gives students the chance to reflect on their learning. (Best, 2021)

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Fluency builds the foundations students use to tackle more complex, multi-step questions in problem-solving and reasoning activities, and it’s crucial to their success.

-Mathematical fluency saves energy (saving more energy for the harder problems)
-Mathematical fluency saves time (which is beneficial in test-taking scenarios and helps focus)
-Mathematical fluency builds confidence and reduces math anxiety, and
-Early mathematical fluency will help the development of math concepts later.

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In summary: Mathematical fluency skills help students think faster and more clearly, giving them the energy, attention and focus to tackle complex problem-solving and reasoning questions.

The future needs problem-solvers with reasoning skills. But as education shifts its focus to the critical and creative angle of mathematics problems, we can't lose sight of the abilities and skills that make this thinking possible: mathematical fluency.

We've covered mathematical fluency in another article ( What is mathematical fluency?), but here's the TL;DR version:
Mathematical fluency is the ability to quickly and accurately recall mathematical facts and concepts. It's made up of 5 key parts - accuracy, flexibility and appropriate response, efficiency, automaticity, and number sense.
Fluency builds the foundations students use to tackle more complex, multi-step questions in problem-solving and reasoning activities, and it's crucial to their success. Here's why:

Mathematical fluency saves energy

Students have only so much energy. You'll have noticed this before and after lunch breaks. The same principles apply when it comes to problem-solving and reasoning activities.

Let's say your PSR activity has five steps, and each one of them has four or five problems to solve. The more energy students spend on figuring out those smaller questions, the less they'll have when it comes to critically and creatively tackling the whole question.

Further, when students aren't succeeding at one part of a larger problem, it can make the entire activity seem like an overwhelming exercise.

If we're to look at a student's brain, those with high fluency skills would have efficient neural pathways, meaning there's less energy spent and less time is taken for the question to be received and for the answer to be found.

The good news is that these neural pathways are strengthened with repeated exercise, like with any learned behaviour.

By getting students to practice fluency, you're strengthening the mind muscles they need to do heavier lifting and for longer.

Fluency saves time

Hand-in-hand with saving energy, fluency saves time for students, and this has two distinct benefits: it helps students stay focused on the logical progression of problems and perform better on tests.

Focus - In a multi-step problem that asks students to use several approaches (like a mix of geometry, algebra, fractions and so on), being able to recall or solve the minutiae with little or no effort keeps them from losing focus on their logical progression.

It's like being on a hike where you're expected to find your food and water, camp, and mountain climb - if you're stuck focusing on each step and breathing in and out, you probably won't feel much like setting up a tent or getting your ropes and climbing gear in order.

Better test-taking - Tests have time limits and they're stressful. Fluency alleviates these pressures; first, by enabling students to attempt to complete more questions, and by getting around the roadblocks of basic computations (like counting on fingers, writing down, working out or reaching for the calculator).

Math fluency builds confidence and reduces mathematics anxiety

Motivation, engagement and progress all rely on students' confidence that they can complete tasks. For students with mathematics anxiety (the feeling of being overwhelmed or paralysed by mathematics), this is especially important.

Strong fluency allows students to work and see success independently, growing their sense of autonomy and confidence, and helping them see whole problems as small, achievable steps.

It's like any kind of sporting competition or arts performance; the drilled basics allow the athlete or artist to work on more complicated movements and strategies and prepares them mentally for big events.

In this case, our events are tests, problem-solving, or being introduced to new concepts and material.

Early mathematical fluency is an indicator of later success

Students who have better fluency in their early education are likely to perform better as they enter secondary school. But it goes further than that - mathematically fluent early learners see significant gains in their mathematics achievements later on.

We can make educated guesses for why this is - the pace of education and the progressive complexity of mathematics means that those who don't develop strong fluency early will have a harder time keeping up.

This is especially true when it comes to problem-solving and reasoning.

Preparing students early with fact fluency gives them the tools they need to take on the harder problems they'll inevitably face in their secondary schooling. If we don't, it's like throwing an entry-level karate student into the ring with a black belt master - they won't have the strategy, reflex or thinking to take them on.

Mathematical fluency prepares students for the problem-solving future

It's hard to imagine what the future careers of our students will look like. But judging by the push into an automatic world, we can almost guarantee they'll need three key things to be successful:

The ability to understand and manipulate data

Critical thinking skills that will allow them to act strategically and tactically

Creative thinking skills that enable them to approach problems in a variety of ways

How to reinforce your students' mathematical fluency

We recommend three things:

Playing mathematics games

Practice requires repetition, and repetition is fun when it's gamified. But games have a few further benefits:

They encourage thinking about mathematics on a strategic level

They need less teacher input and encourage autonomous learning

They build students computational fluency

They connect the classroom environment to the home learning environment

Daily mathematics fluency activities

Mathematics skills become strong when they're done regularly. After a concept has been introduced, you should look to have activities planned to cement students' knowledge until you're confident they can work on it or use it independently.

Give students time to discover

Plan lessons that allow students time to discover number patterns, structures, and concepts and test them out in different situations to see if what they discovered works. This builds autonomy and gives students the chance to reflect on their learning.

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Here's Why Mathematical Fluency is Critical For Problem-Solving and Reasoning - 3P Learning

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In summary: Mathematical fluency skills help students think faster and more clearly, giving them the energy, attention and focus to tackle complex problem-solving and reasoning questions. The future needs problem-solvers with reasoning skills. But as education shifts its focus to the critical and creative angle of mathematics problems, we can't lose sight of the abilities [...]

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Achieving access and equity requires that all stakeholders—

ensure that all students have access to a challenging mathematics curriculum, taught by skilled and effective teachers who differentiate instruction as needed;

monitor student progress and make needed accommodations; and

offer remediation or additional challenges when appropriate.

Taking these steps requires that mathematics teachers work collaboratively with other education specialists, including those in special education, gifted education, instructional technology, and English language development. (Access and Equity in Mathematics Education n.d.)

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Application of comprehension in a classroom involves multiple steps. It involves building on students' background knowledge while also supplying students with the knowledge necessary to visualize, infer, question, and summarize. Teachers can teach words and definitions before they read, they can teach text structures, and they can teach strategies to use before, during, and after reading to help aid in text comprehension.

"Teachers can play a critical role in helping students develop their comprehension skills. Reading research has shown that comprehension instruction can help students do a better job of understanding and remembering what they read. Good instruction can also help students communicate with others, verbally and in writing, about what they’ve read." (Reading comprehension 2023)

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When we think about comprehension in mathematics, it's easy to jump right into word problems. This video explains how reading comprehension affects students when solving math problems and explains how to teach students to break it down step by step, modeling your thinking.

However, comprehension in mathematics is more than just solving word problems. "...it is about teaching children to understand,  to comprehend the meaning of symbols, numbers and more. It’s about making connections – a skill also crucial to English success." (Comprehension for English and maths? taking a cross-curricular approach 2018) "Without solid comprehension skills, children who are otherwise strong in maths skills can underperform."

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Improve Comprehension of Math Word Problems

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To support equity and inclusivity, there are a few things to keep in mind.
1. Equity does not mean equal. When considering how equitable one's teaching and expectations are, we must consider the diverse needs and strengths of individual students, as well as the needs and strengths of the whole class.
2. Focus on the individual. The more we understand and respect the individual's background and strengths, the more we understand their particular needs.
3. Create an environment for success. The expectations that we hold for our students send clear messages of how we feel about their education.
4. Identify your biases, and then get over them. As teachers, we are responsible for helping EACH and EVERY student succeed, not just the ones that fit into our "box" of people who should do well.
5. Create an equitable curriculum that supports diverse needs and celebrates diverse strengths. Not every student learns the same way, so we must vary our approaches to lessons and provide students with manipulatives, visuals, projects, technology and group work to reach as many minds as possible.
6. Be aware of your questioning and listening techniques. How we ask questions, who we direct them to, and our interest in student responses can have lasting impacts on our students' achievement. (Supporting Each and Every Student: Equity and Diversity n.d.)

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"The scientific research on vocabulary instruction reveals that most vocabulary is learned indirectly and that some vocabulary must be taught directly." (Vocabulary 2023)  Because of this, application of vocabulary is done in multiple ways. When students learn vocabulary indirectly, it is generally due to reading or engaging in written and spoken language. When students learn vocabulary directly, it is generally taught by breaking the words down into smaller parts and analyzing them, or being directly told the word and definition by someone.

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This video explains how math vocabulary is extremely important, and that it must be taught in a way that is "clear and concise". The video goes on to use the example of the word "negative" and how it has a double meaning. Outside of math, people associate the word "negative" with something bad, however, in math it is an amount that is less than zero.
Other examples are the words, "sum" versus the word "some," and the words, "hole" versus the word, "whole".

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Why Teaching Mathematical Vocabulary Is Important

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I am including this video in this category even though I also included it in another category, because the speaker in the video makes a fantastic point about English Language Learners and their use of vocabulary. We, as educators, must explicitly teach words and definitions to students due to words that sound similar but have different meanings. This can be especially confusing for students whose first language is not English. To scaffold the use of specific vocabulary in math, it would be helpful to have a "word wall" or posters with relevant vocabulary on it for students to reference.

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Why Teaching Mathematical Vocabulary Is Important

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"Different fields of study have different priorities in terms of the writing they produce. For example, in scientific writing it’s crucial to clearly and accurately report methods and results; in the humanities, the focus is on constructing convincing arguments through the use of textual evidence." (What is academic writing?: DOS and don'ts for students n.d.)
Application of writing varies among the disciplines, but the general idea is that writing application involves making use of the correct vocabulary and terminology to convey a coherent point, message, or persuasion.

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"Professional mathematicians spend most of their time writing: communicating with colleagues, applying for grants, publishing papers, writing memos and syllabi. Writing well is extremely important to mathematicians, since poor writers have a hard time getting published, getting attention from the Deans, and obtaining funding. It is ironic but true that most mathematicians spend more time writing than they spend doing math.
But most of all, one of the simplest reasons for writing in a math class is that writing helps you to learn mathematics better. By explaining a difficult concept to other people, you end up explaining it to yourself." (Writing in Mathematics 1994)

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Inclusivity in writing means using the correct terminology when referring to different groups of people. For example, "authors who write about identity are encouraged to use terms and descriptions that both honor and explain person-first and identity-first perspectives. Language should be selected with the understanding that the individual’s preference supersedes matters of style. In person-first language, the person is emphasized, not the disability or chronic condition." (Equity, Diversity, and Inclusion, 2021) The same applies when referring to peoples' cultures, races, ethnicities, and more. (Of course, some people use these descriptors as identifiers; in which case, we should refer to them in the way that they wish). We need to always be mindful of the words we use to ensure inclusivity for all groups of people.