PDF Summary:11 Effective Strategies for Teaching Math to Students Who Have Given Up on Learning, by Jordan B. Smith Jr.

Engaging students who have lost interest in learning math is a major challenge for many teachers. In 11 Effective Strategies for Teaching Math to Students Who Have Given Up on Learning, Jordan B. Smith Jr. provides practical guidance to help re-motivate struggling learners.

The book introduces methods for establishing a supportive classroom environment, fostering students' intrinsic motivation, incorporating relevant technologies and real-world applications, and promoting long-term retention of concepts. Smith also details structured instructional approaches like the Concrete-Representational-Abstract technique and schema-based problem-solving to make complex math accessible.

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Utilizing Speech Recognition, Visual Aids, and Tools That Read Aloud

Don't limit the use of assistive tools to reading and writing tasks—motivate students to apply them across the curriculum, including in math. Text-to-speech is useful for reading word problems aloud, allowing students to concentrate on comprehension rather than decoding. Speech-to-text tools can assist learners who struggle with handwriting by letting them record their reasoning aloud. Visual aids like diagrams, digital manipulatives, or interactive simulations can provide multiple entry points to understanding abstract concepts.

Practical Tips

• Partner with a local tech company to develop a mentorship program where professionals demonstrate the real-world applications of assistive tools in STEM fields. This can help students see the value of these tools beyond the classroom and understand how they are used in various careers, thereby increasing their motivation to master them.
• Use a voice memo app on your smartphone to dictate your thought process while solving word problems. Listening back to your explanations can help identify areas where you might have misunderstood the problem and allow you to correct your approach.
• Create a study group where members use voice recordings to explain concepts to each other. Each person can record their explanation of a topic using speech-to-text, then share the text with the group. This method allows you to see different perspectives on the same topic and can help clarify complex ideas when you read through the various explanations.
• Use free online graphing tools to turn data from your monthly expenses, fitness routine, or any other personal tracking into visual graphs. By doing this, you can better understand trends and patterns in your own life. For example, you might use a line graph to track your daily step count over a month, helping you see how your activity level changes on weekends versus weekdays.

Empowering Students to Own Their Education With Technology

Smith believes technology gives students greater control over their education and lets them customize the experience to suit their individual needs. By providing a menu of tech options, you empower students to make choices tailored to their strengths and learning preferences. For example, a learner with auditory processing difficulties might opt for visual supports like concept mapping software, while someone with dysgraphia might choose speech-to-text to express their mathematical thinking. This sense of agency can boost learners' self-assurance and drive.

Context

• Technology enables collaboration through tools like shared documents and virtual classrooms, allowing students to work together regardless of physical location.
• Technology can provide accessibility features that help remove barriers for students with disabilities, ensuring that all students have equal opportunities to succeed.
• This refers to challenges in the brain's ability to process and interpret sounds, which can affect how individuals understand spoken language, even if their hearing is normal.
• Many modern devices, including smartphones, tablets, and computers, come equipped with built-in speech-to-text capabilities, making this technology widely accessible to students who need it.

Connecting Mathematical Concepts to Authentic, Relatable Scenarios

Smith stresses the significance of demonstrating that math isn’t solely concerned with abstract formulas and procedures; it's a tool for understanding and navigating the world around us. He recommends creating projects that involve practical applications, like planning a budget for a class event, designing a scale model of a building, or analyzing data from a scientific experiment.

Engaging Students Through Interactive Projects and Simulations

Smith suggests incorporating interactive projects and simulations that let learners apply mathematical concepts in authentic situations. Setting up a mock stock market where students track earnings and make investment decisions might be more engaging than working through equations in isolation. Using online tools like GeoGebra to explore geometric principles interactively or creating simulations to model probability scenarios can make ideas that are abstract come alive.

Practical Tips

• Create a math-themed escape room challenge using household items to solve puzzles that require mathematical reasoning. For example, you could set up a series of locks that can only be opened by solving algebraic equations or geometry problems. This turns abstract math concepts into tangible tasks that must be completed to 'escape' the room.
• Develop a personal investment journal to track hypothetical trades and market observations. This can be a simple spreadsheet or a dedicated app where you record your investment decisions, the reasoning behind them, and the outcomes if they were real. Over time, you'll have a record of your learning progress and can identify patterns in your decision-making process, helping you to understand the market better.
• Create a digital art piece using geometric principles by manipulating shapes and patterns in a graphic design software. By experimenting with symmetry, tessellation, and transformation, you can gain a deeper understanding of geometry while expressing creativity. For example, design a wallpaper for your computer or a unique print for a T-shirt by arranging geometric shapes in an aesthetically pleasing manner.
• Use board games with probability elements to visualize outcomes and decisions. Board games like Risk or Settlers of Catan involve chance and strategy, which can help you understand probability in a tangible way. By playing these games, you can observe how different strategies lead to different outcomes and get a feel for how probability affects decision-making in a controlled, risk-free environment.

Highlighting Math's Practical Applications

Whenever introducing a new concept, Smith recommends making an effort to connect it to a practical use or profession. When teaching about proportionality and ratios, discuss careers in architecture or engineering that rely on these concepts. When covering data analysis, talk about how statisticians and researchers use these abilities across different fields. By highlighting the tangible ways math impacts our lives and society, you can spark students’ curiosity and help them recognize the importance of what they’re learning.

Context

• Providing historical examples of how math has been applied in various fields can give students a deeper appreciation of its development and significance over time.
• Both architects and engineers use ratios to assess environmental impacts, such as energy efficiency and resource use, to create sustainable designs.
• Statisticians evaluate player performance, develop strategies, and improve team management by analyzing game data and player statistics.
• Math enhances critical thinking and logical reasoning skills, which are valuable in everyday decision-making and problem-solving beyond academic settings.

Implementing Useful Instructional Methods

Beyond creating a positive environment and fostering motivation, Smith provides practical methods to guide students toward success. Two of the key strategies he champions are the Concrete-Representational-Abstract (CRA) approach and schema-based problem-solving. These methods provide structured frameworks for deconstructing intricate concepts, making them accessible to learners with diverse needs.

Employing the CVA Approach: Concrete, Visual, and Abstract Steps

Smith believes that many special needs students best grasp mathematical concepts by moving from concrete experiences to abstract representations. The CVA approach lays out a straightforward path for this journey. He recommends starting with concrete manipulatives, like counters or blocks, to show numbers and operations physically. Once students have a foundation in the concrete, visuals like drawings or diagrams help them make the connection to more abstract symbols and numbers.

Using Manipulatives to Develop Foundational Understanding

When introducing new concepts or operations, let students work with objects to build understanding. For example, when teaching addition, give each student some blocks. You might then say "Let's add 3 blocks and 2 blocks together. Combine your blocks and count how many there are altogether." This enables learners to see and feel the addition process before moving to writing equations. Smith emphasizes that this concrete experience makes abstract operations less intimidating.

Practical Tips

• Transform your garden into a living graph for data collection and analysis. Assign different sections of the garden to represent categories of data, such as types of plants or growth rates. Use colored stakes or markers to represent different data points. Over time, you can observe, measure, and record the growth, visually comparing the results in a real-world, hands-on manner. This approach can help you understand concepts like averages, variances, and trends in a tangible way.
• Create a storytelling game where children use random objects to build scenes or characters as they narrate a story. This can enhance their creativity and understanding of narrative structure while also improving their ability to associate physical objects with abstract ideas.
• Encourage a "build and add" play session with children using blocks or LEGO. Set challenges where each block represents a number, and constructing a structure involves adding those numbers together. For instance, if one block equals one unit, challenge them to build a tower that's ten units high using only towers of smaller heights that they have to add together.
• Turn everyday chores into counting opportunities by assigning a number to tasks and tracking the cumulative total. For example, if you're organizing your bookshelf, count each book as you place it. Keep a tally for the day and see how many objects you've handled by the end of your chores.
• Build simple physical models to understand complex systems. If you're learning about ecosystems, you could use a combination of plants, soil, and water in a transparent container to create a small-scale model of an ecosystem. Observing how these elements interact over time can demystify the abstract concept of ecological balance.

Transitioning From Tangible Representations to Imagery and Abstract Concepts

Once learners thoroughly grasp concepts concretely, shift to visual depictions. Drawing simple diagrams on the board or giving students printed worksheets depicting blocks or counters can act as a bridge between physical materials and abstract symbols. You might say, "Now instead of using actual blocks, let's draw circles to stand for them. If we draw 3 circles and then 2 more circles, how many do we have in total?" Finally, introduce numerical representations and equations. You could ask, "How can we write what we just did with circles using numerals and a plus sign?" This gradual progression helps learners connect concrete experiences with abstract symbols.

Practical Tips

• Create a personal symbol dictionary by drawing simple icons that represent complex ideas or tasks in your daily routine. For example, sketch a watering can to symbolize plant care or a book to denote reading time. This visual shorthand can help you quickly organize and process your to-do list or goals by bridging the gap between concrete actions and abstract planning.
• Create a printed worksheet for your monthly budget using counters to represent different expenses. Assign a specific shape or color to each type of expense, such as triangles for groceries or red counters for utilities. This can help you visualize where your money is going and make it easier to identify areas where you can cut back. For instance, if you see a large number of red counters, you might realize you're spending too much on electricity and look for ways to save energy.
• Create a circle-based mood tracker in your journal. Draw a large circle for each week, and divide it into seven segments. Color in each segment based on your mood for the day, using different colors to represent different moods. This will help you visualize patterns in your emotional well-being over time.
• Use cooking as a way to practice converting visual representations into numerical expressions. When following a recipe, visualize the ingredients as parts of a whole — like a pie chart — and then calculate the fractions or percentages needed for each ingredient. This could be particularly helpful when adjusting recipes for more or fewer servings.
• Start a hobby that involves measurements and precision, like baking or model building, where you must follow numerical recipes or instructions. This will not only improve your ability to work with numbers but also give you a practical understanding of how small changes in quantities can lead to different outcomes.
• Create a visual metaphor that represents an abstract idea, using objects from your daily life. For example, to explain the concept of a network, you could arrange household items like strings and nails on a board to represent nodes and connections. This visual aid can serve as a conversation piece to discuss the abstract idea of networking with others who might find the concept challenging to grasp.

Helping Students Use Schema-Based Problem Solving

Smith advocates teaching students problem-solving strategies based on identifying the underlying structure or "schema" of various word problems. By recognizing the common elements across questions, learners can apply a consistent, systematic approach instead of feeling intimidated by each new one.

Identifying the Structure and Components of Types of Problems

Smith advises you to explicitly instruct students in analyzing verbal questions and identifying key information. For instance, "compare" problems involve finding the difference between two sets, and you can teach students to identify keywords like "more than" or "less than." Similarly, "part-part-whole" problems describe a total made up of parts, and learners can recognize phrasing like "in all" or "altogether." By categorizing problems, you equip them with strategies to tackle them confidently.

Other Perspectives

• Some compare problems may use more complex language or present comparisons implicitly, without using keywords like "more than" or "less than," which could leave students unprepared for these scenarios.
• Teaching students to recognize specific phrases may not always be effective, as the same mathematical concepts can be presented using different terminology or in a context where those phrases are not used.
• Relying too heavily on problem categories could stifle creativity and critical thinking, as students might not learn to approach problems from multiple angles.

Supporting and Offering Opportunities for Guided Practice

When introducing new types of problems and their corresponding schemas, Smith emphasizes the need for scaffolding and guided practice. Give students partially completed problems, visual supports, or sentence starters to assist in structuring their thinking. Working through example problems together as a class, guiding students through every stage of the schema, allows you to find parts that may confuse students and offer immediate support. Gradually decrease the level of support as learners gain independence.

Context

• Sentence starters are prompts that help students begin their responses or thoughts, particularly useful in structuring written or verbal explanations, thereby enhancing their ability to articulate mathematical reasoning.
• This refers to the amount of working memory resources required to perform a task. By breaking down problems and providing supports, teachers can help manage cognitive load, making it easier for students to process and understand new information.
• Teachers can model effective problem-solving strategies, demonstrating how to approach complex problems systematically, which students can then emulate.
• Students often struggle with identifying which part of a problem corresponds to each element of a schema. This confusion can arise from a lack of familiarity with the problem type or insufficient practice with similar problems.
• This strategy is part of differentiated instruction, where teaching is tailored to meet the diverse needs of students, allowing them to progress at their own pace.

Promoting Retention and Recall of Math Information

After students grasp concepts, the challenge becomes helping them retain information long-term. Smith stresses that traditional methods of studying, like reading textbooks or jotting down notes, are often ineffective for learners with special needs. He recommends incorporating retrieval exercises and spaced repetition to solidify learning and make knowledge "stick." Additionally, he suggests exploring alternative study techniques, like the Feynman and Pomodoro methods, and empowering students to discover what suits them most effectively.

Incorporating Recall Exercises and Spaced Repetition

Smith champions regularly incorporating retrieval practice into your lesson plans. Rather than waiting for a summative test, frequent low-stakes assessments require learners to recall content actively, which strengthens memory. You might do this by beginning each class with a brief recap of the previous lesson's main ideas.

Frequent, Low-Stakes Evaluations to Reinforce Learning

Smith suggests incorporating low-stakes quizzes, exit tickets, or even quick whiteboard brainstorming sessions to support students in regularly practicing retrieving information. This not only reinforces learning but also provides you with immediate feedback about what students are grasping and which areas require more review. These assessments aren’t required to be graded; the focus should be on the practice of recalling and applying the material.

Context

• Regular retrieval practice helps strengthen memory and improve long-term retention of information, as it encourages students to recall and apply what they have learned.
• These evaluations are designed to reduce anxiety and pressure associated with high-stakes testing, allowing students to focus on learning rather than performance.
• Timely feedback can boost student motivation by showing them their progress and helping them feel more confident in their abilities.
• These activities can increase student engagement by making learning more interactive and less intimidating.

Distributing Study Sessions to Enhance Long-Term Memory

Spaced repetition, another technique advocated by Smith, involves revisiting content at increasing intervals. You might review a new idea the day after it's introduced, then again a week later, then a month later. This spaced approach is much more effective than cramming all the review into a single session just prior to a test.

Other Perspectives

• The strategy may not be as practical or feasible for learners with tight schedules or those who are managing multiple subjects, as it requires careful planning and time management.
• The intervals suggested (the day after, a week later, a month later) may not be optimal for all learners or all types of information; some learners might benefit from shorter or longer intervals between study sessions.

Empowering Learners Through Varied Study Techniques

Smith suggests that you equip learners with a variety of study techniques so they can discover what suits them best. Beyond traditional note-taking, encourage them to create mind maps, use flashcards, teach each other the concepts, or even create videos teaching the material.

Methods: Feynman and Pomodoro Techniques

The Feynman Technique, which takes its name from physicist Richard Feynman, involves having students explain a concept in simple terms, as if teaching it to someone with no prior knowledge. This forces them to clarify their own understanding and pinpoint points of uncertainty. For learners who have trouble with focus, Smith recommends trying the Pomodoro Technique, which involves working in 25-minute intervals followed by short breaks. This method aids in maintaining concentration and preventing burnout.

Other Perspectives

• The technique may not address different learning styles effectively, as it primarily focuses on verbal and linguistic intelligence.
• Simplifying a concept does not necessarily mean a student has a deep understanding of the subject; they might still be missing nuances or advanced applications.
• Some people may find the 25-minute work interval too short to fully immerse themselves in complex tasks, which could lead to decreased productivity.
• The effectiveness of the Pomodoro Technique can vary greatly depending on the person's work style, discipline, and the nature of the task at hand.

Helping Students Discover Their Best Approach

Smith emphasizes that there is no single "best" learning method for everyone. Urge learners to try different techniques and reflect on what helps them learn most effectively. You could offer a "study menu" of options, guide them through a self-assessment of their learning preferences, or provide opportunities to share strategies that have worked for them.

Practical Tips

• Use a habit-tracking app to set reminders for self-reflection on learning methods. Choose an app that allows you to customize reminders and input notes. Set it to prompt you at the end of each learning session to record which methods you used and rate their effectiveness on a scale. This will help you to quickly identify the most effective strategies without relying on memory alone.
• Use a random topic generator online to challenge yourself with new and unexpected subjects to learn about each week, reflecting the variety of a study menu. Set aside dedicated time to research and explore whatever topic comes up, using resources like online courses, local library books, or expert interviews. This strategy keeps your learning dynamic and can expose you to subjects you might not have chosen on your own.
• Create a personalized learning inventory by listing activities that engage you and those that don't, then adjust your study habits accordingly. For example, if you find that you're more engaged when using visual aids, incorporate more diagrams and videos into your study sessions. Conversely, if traditional note-taking bores you, try converting your notes into mind maps or infographics.
• Create a digital story map where students can pin their successful learning strategies along with a brief anecdote or example of how it worked for them. This visual and interactive tool allows students to explore different strategies in a context that feels personal and relatable. For instance, a student who excels in history might share a strategy using a story map point located at a historical site they visited, explaining how the visit enhanced their learning.

Lesson Planning and Implementation

Bringing it all together, Smith stresses that effective math instruction for learners with special needs requires careful planning that incorporates the strategies and principles outlined throughout the book. He encourages you to match lesson objectives to both educational benchmarks and students' individual needs. He also recommends designing multi-sensory, engaging learning experiences that cater to diverse learning styles and adjusting plans based on your observations of students' progress.

Aligning Goals With Requirements and Necessities

Smith suggests starting your planning process by looking at both the required curriculum standards and your students' IEP goals. Aligning your lesson objectives with these goals ensures your instruction is both rigorous and tailored to every student's unique needs.

Determining Required Skills and Providing Support Effectively

Once objectives are set, Smith highlights the necessity of carefully analyzing what prerequisite skills students require to succeed. He recommends considering, "What knowledge or abilities must students have before they can tackle this new concept?" Then, plan instruction, exercises, and evaluations that build upon and reinforce those core abilities. During instruction, the author strongly advises you to provide appropriate scaffolding to support students with diverse needs, like visual aids, simplified instructions, or diagrams that structure information.

Context

• This strategy aligns with the backward design model in education, where educators start with the end goals and work backward to develop curriculum and instruction.
• Understanding prerequisite skills helps ensure that students have a solid foundation, preventing frustration and disengagement when new material is introduced.
• The main goal of scaffolding is to provide support to students as they develop new skills or understand new concepts, gradually removing the support as students become more proficient.
• These are visual representations that can illustrate relationships between concepts, such as flowcharts or mind maps, helping students organize and retain information.

Incorporating Adaptability and Accommodations to Aid Diverse Learners

Smith emphasizes that flexibility is necessary throughout both planning and implementation. He recognizes that special needs students might require accommodations like extended time, modified assignments, assistive technology, or alternative assessment formats. Building flexibility into your plans, like including optional extension activities or adjusting pacing based on student needs, allows you to customize the learning experience to best foster each student's growth.

Context

• Teachers can better manage and allocate resources, such as time and materials, to ensure that all students have what they need to succeed, especially in under-resourced settings.
• Instead of traditional tests, students might demonstrate understanding through projects, oral presentations, or portfolios, which can be more suitable for those who struggle with standard testing methods.
• Integrating SEL into the curriculum helps students develop self-awareness, self-control, and interpersonal skills, which are essential for success in school and life.

Designing Engaging Activities That Stimulate Multiple Senses

Smith argues that, to capture students' attention, you need to move beyond traditional lecture-style teaching. He encourages you to incorporate hands-on activities, real-world projects, collaborative tasks, and technology to create multi-sensory learning experiences that appeal to different learning styles and keep students actively participating.

Selecting Appropriate Instructional Methods and Materials

When designing lessons, carefully consider how YOU’ll present information and what resources you'll use. Smith suggests incorporating a variety of instructional methods, like direct instruction, modeling, guided practice, and work done individually. He also recommends choosing materials that are appealing to the eye, tactile, or auditory, based on what your students need and prefer.

Other Perspectives

• Overemphasis on presentation can lead to style over substance, where the way information is delivered becomes more important than the information itself.
• Individual work, while valuable, may not always be the best approach for students who thrive on collaboration and could lead to feelings of isolation or lack of support.
• Materials that are visually appealing, tactile, or auditory could potentially become distractions if not integrated thoughtfully into the lesson plan.

Monitoring Student Progress and Adjusting Plans as Needed

Even with the best planning, no lesson is perfect for all students every time. Smith encourages you to be adaptable and responsive to what students need. He suggests regularly monitoring student development through informal observation, checking for understanding during lessons, and incorporating frequent formative assessments. Don't be afraid to change your plans based on what you observe, whether that means revisiting an idea, offering more scaffolding, or supplying alternative educational pathways.

Context

• Regular informal observation can help build trust and rapport between students and teachers, as students feel seen and understood in their learning journey.
• Digital tools and platforms can facilitate checking for understanding through interactive polls, quizzes, and real-time feedback, making the process more engaging and efficient.
• By incorporating formative assessments, teachers can be more responsive and flexible, adapting their teaching strategies to better align with student needs and learning styles.
• Students come from diverse cultural backgrounds that can influence their learning experiences and perspectives. Being responsive involves acknowledging and respecting these differences in the classroom.
• Students' emotional and social states can impact their learning. Being responsive to these factors by adjusting plans can create a more supportive and effective learning environment.
• This means offering different methods or approaches to learning that cater to diverse student needs and learning styles. It can include using technology, project-based learning, or hands-on activities. Alternative pathways aim to engage students by aligning with their interests and strengths, making learning more accessible and personalized.