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5.6.3: Effective Reading Strategies - Mathematics


Figure (PageIndex{3}): If you plan to make time for reading while you commute, remember that unexpected events like delays and cancellations could impact your concentration.

Example Reading Times
ReaderPages Read in 5 MinutesPages per HourApproximate Hours to Read 500 Pages
Marta44810 hours, 30 minutes
Jordi33613 hours
Estevan5608 hours, 20 minutes
Example Active Reading Times
ReaderPages Read in 5 MinutesPages per HourApproximate Hours to Read 500 PagesApproximate Hours to Actively Read 500 Pages
Marta44810 hours, 30 minutes21 hours
Jordi33613 hours26 hours
Estevan5608 hours, 20 minutes16 hours, 40 minutes

Figure (PageIndex{4}): The six elements of recursive reading should be considered as a circular, not linear, process.


Figure (PageIndex{5})

Figure (PageIndex{6})

Figure (PageIndex{7})

Figure (PageIndex{8}): Learning about the book you’re reading can provide good context and information. Look for an author’s biography and forward on the back cover or in the first few pages. (Credit: Mark Hillary / Flickr / Attribution 2.0 Generic (CC-BY 2.0))


Tips for Effectively Teaching Reading

Teaching reading is both an art and a science. Teachers everywhere understand the art aspect: you must watch children and know when to put the right book in the right hands or teach the right strategy at the right time. The science aspect involves learning effective teaching strategies to build literacy development throughout the year. In order for students to read well, they must be able to do the following:

  • Understand letter sounds and use them to read and spell words.
  • Practice reading enough to become fluent readers.
  • Learn new vocabulary words.
  • Learn to self-monitor when reading for comprehension and errors.

Teach the Seven Strategies of Highly Effective Readers

By: Elaine K. McEwan

To improve students' reading comprehension, teachers should introduce the seven cognitive strategies of effective readers: activating, inferring, monitoring-clarifying, questioning, searching-selecting, summarizing, and visualizing-organizing. This article includes definitions of the seven strategies and a lesson-plan template for teaching each one.

To assume that one can simply have students memorize and routinely execute a set of strategies is to misconceive the nature of strategic processing or executive control. Such rote applications of these procedures represents, in essence, a true oxymoron-non-strategic strategic processing.

&mdash Alexander and Murphy (1998, p. 33)

If the struggling readers in your content classroom routinely miss the point when "reading" content text, consider teaching them one or more of the seven cognitive strategies of highly effective readers. Cognitive strategies are the mental processes used by skilled readers to extract and construct meaning from text and to create knowledge structures in long-term memory. When these strategies are directly taught to and modeled for struggling readers, their comprehension and retention improve.

Struggling students often mistakenly believe they are reading when they are actually engaged in what researchers call mindless reading (Schooler, Reichle, & Halpern, 2004), zoning out while staring at the printed page. The opposite of mindless reading is the processing of text by highly effective readers using cognitive strategies. These strategies are described in a fascinating qualitative study that asked expert readers to think aloud regarding what was happening in their minds while they were reading. The lengthy scripts recording these spoken thoughts (i.e., think-alouds) are called verbal protocols (Pressley & Afflerbach, 1995). These protocols were categorized and analyzed by researchers to answer specific questions, such as, What is the influence of prior knowledge on expert readers' strategies as they determine the main idea of a text? (Afflerbach, 1990b).

The protocols provide accurate "snapshots" and even "videos" of the ever-changing mental landscape that expert readers construct during reading. Researchers have concluded that reading is "constructively responsive-that is, good readers are always changing their processing in response to the text they are reading" (Pressley & Afflerbach, 1995, p. 2). Instructional Aid 1.1 defines the seven cognitive strategies of highly effective readers, and Instructional Aid 1.2 provides a lesson plan template for teaching a cognitive strategy.


2. Explicitly Teach and Display Strategies

We all know that amazing feeling that comes with creating the perfectly decorated classroom. Everything is in its place and perfectly organized – until the kids get there, of course.

But when it comes to room décor, it shouldn’t just be pretty – it should be meaningful. You can make your classroom décor a powerful part of your reading curriculum by displaying strategies around the room.

Displaying and explicitly teaching strategies that your students can use while reading. By keeping useful strategies displayed, you allow your students an element of independence. They can take control of their own reading and help themselves get through tough words or pronunciation issues!

Plus, depending on what strategy posters you decide to use, you can add to the adorable-ness of your room! These Reading Strategy Posters are so useful to both teachers and kids! They offer your students purposeful and specific strategies with beautifully illustrated designs!

You can even purchase the bundle and give each student their own set of strategy cards or keep sets in your reading corner for shared use!


Examples of sources

Peer-reviewed journal articles:

Carnine, D. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.

Cawley, J., Parmar, R., Foley, T., Salmon, S., & Roy, S. (2001). Arithmetic performance of students: Implications for standards and programming. Exceptional Children, 67, 311-330.

Fuchs, L., & Fuchs, D. (2001). Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research & Practice, 16, 85-95.

Maccini, P., & Gagnon, J. (2002). Perceptions and application of NCTM Standards by special and general education teachers. Exceptional Children, 68, 325-344.

Other helpful sources:

Curriculum and evaluation standards for school mathematics. (2000). Reston, VA: National Council for Teachers of Mathematics.

Fuchs, L., & Fuchs, D. (2003). Enhancing the mathematical problem solving of students with mathematics disabilities. In H. L. Swanson, K. R. Harris, & S. Graham (Eds.), Handbook of Learning Disabilities (pp. 306-322). New York: Guilford.

Geary, D. C. (1996). Children&aposs mathematical development. Washington, DC: American Psychological Association.

Rivera, D. P. (1998). Mathematics education for students with learning disabilities: Theory to practice. Austin, TX: Pro-Ed.

Stein, M., Silbert, J., & Carnine, D. (1997). Designing effective mathematicsinstruction: A direct instruction approach (3rd edition). Upper Saddle River, NJ: Merrill.


Tips for Parents of Preschoolers

For preschoolers in the United States, the pressure is on to learn math early and learn it well. The No Child Left Behind Act (NCLB) has put pressure on schools to make sure that all students are meeting state standards for achievement, and this has resulted in more rigorous math curricula and testing, starting in early elementary school. With increased public attention on the value of high-quality early childhood education, the pressure to perform has trickled down to our youngest students, and preschools are taking a closer look at their math programs and making adjustments that will prepare “little learners” for the challenges of elementary school. And parents are always searching for better ways to boost their youngsters’ mastery of early math.

Sound overwhelming? It’s a tall order, to be sure. We can start by learning from some of the research studies on early math acquisition. And we must understand and respect how preschool students naturally explore and experiment with math concepts with this insight, we can identify effective math programs and tailor experiences and instruction that will propel them towards success. Finally, math is best taught at both home and at school. Parents and teachers can work together to make math a fun part of every preschooler’s day.

The many dimensions of math

Even for young children, math is more than just a numbers game. Math has many dimensions, including:

  • Number sense (e.g., the numeral “4” represents four objects, which is greater that 3 and less than 5)
  • Geometry (e.g., patterns and shapes, each with unique features)
  • Measurement (e.g., size, distance, amount)
  • The language of math (e.g., more than, less than, equal to)
  • Spatial relations (e.g., in front of or behind near or far)

Preschoolers learn math by exploring their world

Much attention and research has been focused on early reading over the past few decades and researchers are now catching up to learn more about early math learning and instruction. What they’ve learned so far is intriguing. For example, researchers have found that young children are, by nature, curious about math. They have good evidence that math becomes real to young children as they use it by talking, reasoning, playing, and doing. And, they have a better understanding of how preschoolers’ early exploration of math helps them make sense of their world and what kinds of instruction and practice are needed to help them build new skills and deepen their knowledge.

One somewhat surprising research finding is that preschoolers appear to learn math concepts and operations in a much less predictable sequence than they do when learning to read. Most young children acquire reading awareness and skills in a fairly linear fashion. Think of it this way: Imagine a tower of blocks, with necessary skills — like print awareness — providing a foundation on which to build other skills — like phonemic awareness. Early math learning, on the other hand, is more like assembling a jigsaw puzzle, with children mastering math concepts in no set sequence but still managing to assemble the complete picture over time. While there is no agreed-upon continuum for learning early math, researchers have identified areas of math learning with specific “growth points” that young children achieve as they become more skilled math learners . (These findings are based on the work of the National Mathematics Advisory Panel and the Early Childhood Mathematics project of the National Academy of Sciences.)

Gauging a preschooler’s grasp of math

Preschoolers may learn about math through a variety of pathways, but by age 3 or 4 a child should have a good grasp of certain math concepts and be able to perform basic math operations. (Learn more about these early math benchmarks). Keep in mind that a child may be strong in some aspects of math but have difficulty with others. Some math skills and operations call upon “non-math” skills, such as reading text, fine motor skills, and memory. Be sure to consider all of your child’s academic strengths and weaknesses when searching for the root cause of a possible math problem. Preschool teachers should use basic math assessment techniques to determine a baseline for the student’s math literacy level doing so will help inform decisions about what to teach and how to monitor progress. (Learn more about teaching preschool math). And parents should be invited (and encouraged) to share with the teacher what they know about their child’s basic math abilities and attitudes.

At this time, researchers haven’t been able to clearly identify the core deficits that explain math disabilities in preschool students. While this can make screening and assessment in math tricky, it’s still wise to seek help and additional support for children who display possible signs of a learning disability or delay in math.

The power of a good preschool math program

As states revamp their preschool math program requirements and schools look to strengthen math instruction for students across the grades, parents and educators can play an important role in ensuring that practices that have proven to be effective in promoting math learning are in place:

  • Collect baseline information. Know what concepts and skills a child has already learned so that an effective program of instruction and support can be designed and implemented early in the preschool year.
  • Children will need different types of instruction and support. Teachers will want to meet students “where they are” and tailor instruction to build on the individual child’s knowledge and ability.
  • Make math real. Be sure to reinforce and practice math learning throughout the day, in school, at home, and in the community.
  • Learn math by living math. Focus less on passive learning (such as listening to someone explain and demonstrate), and provide lots of hands-on activities. Young children (and older ones too!) learn by doing.
  • Forge parent-teacher partnerships. Many parents aren’t sure how to teach their preschoolers math at home. Use parent-teacher conferences to discuss strategies that have been successful in the classroom and talk about how these can be reinforced in everyday games and activities at home.
  • Show me the research! Ask why the school uses a particular approach or set of activities to teach math, and ask whether it is based on the best available research.

Math across the curriculum and throughout life

Math is often treated as a one-dimensional subject that is separate from other subjects taught in school. Unfortunately, this is a common (sometimes unconscious) perspective among adults, including preschool teachers and parents. As a result, many preschoolers come to view math as something that has no connection to other school activities or to their daily lives. Adults can correct this kind of “disconnect” by:

  • becoming more aware of how math is part of their personal and professional lives
  • blending math instruction with other subjects (e.g., reading a story that involves counting in some way)
  • broadening the teaching of math to include activities at home and in the community.

Parents + teachers = A winning team

Parents and teachers should work together to assure that each child is learning the many aspects of math – in the classroom, at home, and in the community. Building on a child’s natural interest in math is key, as is monitoring a child’s progress and making adjustments in instruction to address difficulties in understanding and mastering early math concepts. There’s every reason to believe that today’s preschoolers can grow up to understand, experience and appreciate math in a broader and more practical context than the generations before them. We’re counting on it!


Kristin Stanberry is a writer and editor specializing in parenting, education, and consumer health/wellness issues. Her areas of expertise include learning disabilities and AD/HD, topics which she wrote about extensively for Schwab Learning and GreatSchools.


Vocabulary-Building Techniques

Gaining confidence with unique terminology used in different disciplines can help you be more successful in your courses and in college generally. In addition to the suggestions described earlier, such as looking up unfamiliar words in dictionaries, the following are additional vocabulary-building techniques for you to try:

Read Everything and Read Often

Reading frequently both in and out of the classroom will help strengthen your vocabulary. Whenever you read a book, magazine, newspaper, blog, or any other resource, keep a running list of words you don’t know. Look up the words as you encounter them and try to incorporate them into your own speaking and writing.

Make Connections to Words You Already Know

You may be familiar with the “looks like . . . sounds like” saying that applies to words. It means that you can sometimes look at a new word and guess the definition based on similar words whose meaning you know. For example, if you are reading a biology book on the human body and come across the word malignant, you might guess that this word means something negative or broken if you already know the word malfunction, which share the “mal-” prefix.

Make Index Cards

If you are studying certain words for a test, or you know that certain phrases will be used frequently in a course or field, try making flashcards for review. For each key term, write the word on one side of an index card and the definition on the other. Drill yourself, and then ask your friends to help quiz you.

Developing a strong vocabulary is similar to most hobbies and activities. Even experts in a field continue to encounter and adopt new words. The following video discusses more strategies for improving vocabulary.

Words are sneaky, charming, and intriguing. The more complex our vocabularies, the more complex our thoughts are, too.


5 Classroom Strategies for Early Reading Intervention

Today’s students and teachers are under increasing pressure to show early progress and success in reading. Not all of this can be attributed to a desire to increase standardized test scores, as some may fear it also has to do with a concern that kids will be “left behind” if they are not reading independently by at least third grade. This situation often leads to intervention as a strategy for boosting the skills of slow or reluctant readers. But is intervention a one-dimensional tool?

In recent years, the practice of intervention—where a trained reading specialist provides small-group or personalized instruction to students considered to be behind the curve—has been elevated to must-have status. In 2010, Secretary of Education Arne Duncan even listed early literacy intervention (done before students reach third or fourth grade) as a key high school dropout prevention strategy. Many students require early intervention as they find their way to literacy. This support often includes phonics lessons so that children can explicitly learn how to decode words. For some students, such as non-native English speakers, this can be an essential survival skill.

Beyond phonics, there are key intervention strategies that do not necessarily isolate students from one another by sorting them into leveled groups. For example, choral reading is a much-loved way to get the whole class reading along together, which may help less confident readers learn to recognize frequently used words in a more relaxed and community-based manner. A 2014 post in the online journal Edutopia, “11 Alternatives to 'Round Robin' (and 'Popcorn') Reading,” shares a variety of other ways to make learning to read a shared activity. A few highlights include:

1. PALS: ​Peer-Assisted Learning Strategies (PALS) exercises pair strong and weak readers who take turns reading, rereading, and retelling.


2. Teacher Read-Aloud: This activity, says Julie Adams of Adams Educational Consulting, is "perhaps one of the most effective methods for improving student fluency and comprehension, as the teacher is the expert in reading the text and models how a skilled reader reads using appropriate pacing and prosody (inflection)." Playing an audiobook achieves similar results.


3. Shared Reading/Modeling: By reading aloud while students follow along in their own books, the instructor models fluency, pausing occasionally to demonstrate comprehension strategies.


4. The Crazy Professor Reading Game: According to the article, to bring the text to life, students will:

Read orally with hysterical enthusiasm

Reread with dramatic hand gestures

Partner up with a super-stoked question-asker and -answerer

Play "crazy professor" and "eager student" in a hyped-up overview of the text

5. FORI: With Fluency-Oriented Reading Instruction (FORI), primary students read the same section of a text many times over the course of a week. Here are the steps:

The teacher reads aloud while students follow along in their books.

The text is taken home if more practice is required, and extension activities can be integrated during the week.


There is a great deal of evidence to support the idea that students who cannot read well by the time they are eight or nine years old—when the emphasis in school becomes reading to learn and not learning to read—often struggle to catch up both academically and socially with their peers. Fortunately, research and shared best practices available today help teachers develop many different paths to intervention, from creating literacy-rich classrooms to utilizing essential whole group and direct instruction strategies, which can help students become confident, capable, independent readers.

Lexia Core5 Reading ®
Personalized Literacy Instruction for Students of All Abilities

Lexia Core5 Reading supports educators in providing differentiated literacy instruction for students of all abilities in grades pre-K–5. Lexia’s research-proven program provides systematic, personalized learning in the six areas of reading instruction, targeting skill gaps as they emerge and providing teachers with the data and student-specific resources they need for individual or small-group instruction.


Research Shows

  • When paired with cognitive strategies, metacognitive strategies have been shown to increase the understanding and ability of students with mathematics learning difficulties and disabilities to solve mathematics problems.
    (Pfannenstiel, Bryant, Bryant, & Porterfield, 2015)
  • Middle school students who received cognitive and metacognitive strategy instruction outperformed peers who received typical math instruction.
    (Montague, Enders, & Dietz, 2011 Pfannenstiel, Bryant, Bryant, & Porterfield, 2015)

Types of Metacognitive Strategies

Metacognitive strategies that help students plan, monitor, and modify their mathematical problem-solving include self-instruction and self-monitoring. Not only are these strategies relatively easy for students to implement, but they also help students to become better independent problem solvers.

  • “Did I understand what I just read? No, I didn’t. I need to reread the problem.”
  • “What is this problem asking? What information do I have?”
  • “What is the next step?”
  • Checking to make sure all steps are completed
  • Checking for computational errors
  • Checking to make sure the answer is feasible

Teaching Metacognitive Strategies

Teachers should use explicit instruction to help students understand how to use self-instruction and self-monitoring during the problem-solving process. To do this, teachers can:

  • Provide students with a list of questions or prompts to ask themselves while they are engaged in the problem-solving process.
    • Example questions: What information is relevant? Have I solved a problem like this before?
    • Example prompts: Identify the relevant information. Use a visual to solve the problem.

    Examples of Students Using Metacognitive Strategies

    The videos below illustrate students using metacognitive strategies to solve mathematics problems. In the first video, in addition to self-instruction, an elementary student uses an age-appropriate self-monitoring checklist that includes visual cues for each step. Note that the student was explicitly taught how to use this checklist before using it to solve problems independently. In the second video, a high-school student uses self-instruction and self-monitoring to solve a word problem.

    Elementary School Example (time 1:49)

    Transcript: Metacognative Strategies: Elementary School

    Narrator: In this video, an elementary student uses metacognitive strategies while solving an addition problem. More specifically, he uses self-instruction and a self-monitoring checklist to guide himself through the problem-solving process. By doing so, he actively plans and monitors his work.

    Student: I can’t figure out what 3 + 5 is. What is it? Well, let me look at my checklist. First, it says, “read the problem.” The problem says 3 + 5, so I’ve checked that. Now what is…now it says…my checklist says, “What is the problem asking?” It’s asking me to add 3 + 5.

    Now, to draw a picture. One, two, three. One, two, three, four, five. Now it says, “Does my drawing match the problem?” Up here it says 3 + 5, so down here it says one, two, three, one, two, three, four, five. Now I have to solve it. So one, two, three, four, five, six, seven, eight. The answer to 3 + 5 is 8.

    High School Example (time 2:55)

    Transcript: Metacognative Strategies: High School

    Narrator: In this video, a high school student uses metacognitive strategies while solving a word problem. By using self-instruction and self-monitoring, she actively plans and monitors her work.

    Student: First, I’m going to read the problem. “Mr. Smith, the principal, is standing on top of the high school. He is looking at a tree in the courtyard that is 30 feet away from the school. The angle from Mr. Smith’s feet to the base of the tree is 43 degrees. Using this information, determine the height of the high school.”

    So what am I missing? The problem says that the angle from Mr. Smith’s feet to the base of the tree is 43 degrees. I’ve noticed that, if you connect this point to this point, we have a right triangle. So, while this angle is 43 degrees, this angle right here is a right angle that’s 90 degrees.

    There’s a trick that I’m going to use that’s called SOHCAHTOA that you can use to find the sides and angles in a right triangle. The opposite side to 43 degrees is 30 feet, right here. So what do I need to find? I need to find the adjacent side. I’ll label it with an “A.” I look at SOHCAHTOA, and I know that I need to find the tangent, because tangent equals opposite over adjacent.

    Now all I have to do is plug in the information that I have in order to find “A.” Tangent of 43 degrees, the angle, equals 30—that’s the opposite side—over
    “A.” And I find that 30 over 0.93 equals 32.25. So the height of this building is 32.25 feet.

    Now that I’ve solved the problem, I ask does my answer make sense? Given the information from the problem, and with what I know about most buildings, 32 feet seems like a reasonable answer.

    Diane Bryant discusses the importance of teaching students cognitive and metacognitive strategies and how they benefit students (time: 2:23).

    Diane Pedrotty Bryant, PhD
    Project Director, Mathematics Institute for
    Learning Disabilities and Difficulties
    University of Texas at Austin

    Transcript: Diane Pedrotty Bryant, PhD

    It really is important to pair metacognitive strategies with cognitive strategies. Metacognitive strategies simply refers to thinking about thinking. It’s beneficial and certainly validated in research that they have a series of cognitive steps to employ to solve problems, whatever the problem might be. The metacognitive strategies help students think about what steps that they’re supposed to be using—that’s the self-instruction—and then pausing to check about whether they are indeed using those various cognitive strategies steps, which really refers to the self-monitoring. For students with mathematics learning disabilities, we want them to become independent learners and to use strategies for solving various problems and to be able to pause and ask themselves questions about how they’re proceeding and back up and check on a particular step. Through the use of cognitive strategies paired with metacognitive strategies, the goal is to empower them to be more independent learners, and that’s definitely something we strive for when we teach students with learning disabilities. I think that there is difficulty in students learning how to implement metacognitive strategies independently, because they may not know how to approach the learning task. They may not be aware of their own ability to self-monitor, to self-instruct, to use self-talk, self-verbalizations for tackling tasks. Usually students with mathematics learning disabilities really need to be taught to use metacognitive strategies and to learn the metacognitive strategies to mastery before being able to use them independently.


    Teaching Reading: Linking Assessment and Intervention

    There are a number of valuable resources for teaching children with reading problems and reading LDs. The following evidence-based intervention strategies were developed based on a number of important resources, including Berninger & Wolf (2009), Feifer & Della Toffalo (2007), Fry, 2010 Mercer, Mercer, & Pullen (2008), and Shawitz (2005). Several of these intervention strategies recognize the National Reading Panel (2000) findings that effective reading instruction addresses alphabetics, fluency, and comprehenison.


    Watch the video: Reading effectively - a 3-stage lesson guide (November 2021).