We all aspire for our children to excel in mathematics. In many school districts, students’ comprehension is assessed through standardized tests. However, we aim to avoid an excessive focus on test preparation. Relying too heavily on test prep materials and monotonous worksheets not only consumes valuable teaching time but also hampers genuine learning and motivation. Nonetheless, effective teaching and impressive test scores can coexist harmoniously. By purposefully designing your instruction and employing imaginative methods, you can ignite students’ enthusiasm for mathematics. These vital strategies for teaching math have the potential to transform this academic year into your class’s most remarkable math experience ever!
1. Raise the bar for all
To ensure the effectiveness of mathematical strategies, educators must initially instill in students the belief that they have the potential to excel as mathematicians. Maintaining elevated expectations for all students fosters their growth. As early as second grade, young girls may have already absorbed the notion that mathematics is not a subject meant for them. Overcoming the socially ingrained belief of “I’m not good at math” can indeed be challenging, as pointed out by Sarah Bax, a math teacher at Hardy Middle School in Washington, D.C.
Instead of success being determined solely by inherent math talent, it’s crucial for children to hear from their teachers that dedication and hard work can lead to success. Building a growth mindset among students is the key. As Bax aptly puts it, “Practice and persistence are the paths to proficiency in math.” Promoting mathematical equity and enthusiastically conveying to students the power and significance of mathematics, along with setting high expectations, are fundamental aspects of this endeavor.
2. Don’t wait—act now!
Anticipate the particular concepts students must master in preparation for their yearly end-of-year assessments and adjust the pace of your instruction accordingly. Consider the foundational skills that will be essential for the upcoming academic year.
According to Skip Fennell, the project director of the Elementary Mathematics Specialists and Teacher Leaders Project and a professor emeritus at McDaniel College in Westminster, Maryland, it’s crucial not to find yourself unprepared in March, realizing that students should have grasped certain concepts for the tests in the following month. Familiarize yourself with the specific educational standards and work backward in your teaching planning, starting from the beginning of the school year. This way, you can ensure that students are adequately prepared and can implement effective mathematical strategies in your teaching plan.
3. Create a testing pathway
The results of standardized tests may not become available until the following school year, but it’s essential to prepare students for them now. Utilize formative assessments as a means to ensure that students grasp the concepts effectively. The insights you gain from these assessments can serve as a guide for your instruction and help you determine the next steps, according to Skip Fennell.
Rather than implying an endorsement of “teaching to the test,” it’s important to recognize that testing should be an integral part of your instructional planning. Instead of merely using quick exit questions or cards, consider employing methods such as five-minute quizzes, open-ended questions, or meaningful homework assignments to verify that students have indeed mastered the mathematical skills covered in the day’s lesson. Additionally, encouraging students to articulate their thought processes orally or in writing offers a valuable means of assessing their comprehension. A well-designed digital resource, capable of monitoring your students in real-time, can also prove to be an invaluable tool, providing actionable data that can inform your instructional decisions along the way.
4. Observe, modify, and reevaluate
Occasionally, we find ourselves locked into the mindset of covering “a lesson a day” to ensure we progress through the curriculum. Nonetheless, it’s crucial to maintain flexibility in our pacing to prevent students from falling behind. Take a proactive approach by circulating in your classroom as students engage with problems and observe the classroom dynamics. Engage in one-on-one conversations with students and incorporate “hinge questions” into your lesson plans to assess their comprehension before proceeding, as advised by Skip Fennell. Based on the feedback and observations, be prepared to make informed decisions about whether to accelerate the pace, slow down, or organize students into groups as needed.
5. Read, read, read!
While we may not typically associate reading with math strategies, there are few approaches as effective as a captivating read-aloud to prepare students for learning a new mathematical concept. Children have a natural affinity for being read to, and the more we demonstrate the interconnectedness of math with the world around us, the more engaged they become. Incorporating books that highlight mathematical connections during reading sessions helps children recognize how abstract concepts relate to their everyday lives.
6. Personalize and offer choice
When students are granted the freedom to select their preferred learning methods and ways to showcase their comprehension of a concept, their enthusiasm and motivation soar. This approach affords them the opportunity to identify their own learning preferences, empowers them to take control of their education, and provides room for experimenting with diverse problem-solving strategies in mathematics.
Offering students a range of choices, whether it’s through timed exercises, project-based tasks, or utilizing various learning materials, allows them to demonstrate their mastery of foundational skills in a way that resonates with them. As students exhibit their newfound knowledge, educators can effectively gauge their understanding, pinpoint areas where additional support or scaffolding is required, and tailor their lessons accordingly.
7. Plant the seeds!
Don’t leave any child behind! A school garden offers an excellent opportunity to engage students in applying math concepts in an enjoyable manner while instilling a sense of purpose. While it’s evident that topics like measurement, geometry, and data analysis can be effectively addressed through garden activities, don’t overlook the potential to teach operations, fractions, and decimals as well.
Furthermore, garden-based activities can serve as a platform to promote character education objectives such as fostering cooperation, nurturing respect for the environment, and emphasizing the value of giving to others, especially when the crops are donated to organizations that support those in need.
8. Add apps appropriately
The proliferation of apps (interactive software designed for touch-screen devices) aimed at enhancing math instruction has experienced a significant surge in recent years. Children who may be hesitant to engage with traditional pencil-and-paper resources for practicing math facts are often more willing to undertake similar exercises when using a touch-screen interface. Numerous apps primarily center on skill practice through gamified experiences, yet there are also those that actively encourage children to delve into math concepts on a deeper, more conceptual level.
9.Encourage math talk
Engaging in discussions about mathematics plays a crucial role in helping students process new learning and further develop their understanding. Encourage active participation from students by prompting them to explain why they chose a particular approach to solve a problem. Delise Andrews, who has experience teaching math in various grade levels and now serves as a math coordinator in the Lincoln Public Schools in Nebraska, emphasizes the importance of gathering information about students’ thought processes to inform instruction, rather than simply imparting information and expecting rote repetition.
Instead of merely seeking specific answers, Andrews aims for in-depth conversations that uncover what a student truly comprehends. She believes that genuine learning occurs when students engage in discussions and actively practice mathematics, moving beyond mere repetition and drills. It’s essential, however, for students to feel comfortable expressing their mathematical thoughts and to be trained in respectfully listening to their peers’ reasoning.
10. The art of math
Nearly all children have an affinity for art, and it’s important to cater to visual learners by integrating art and math instruction, making it one of the most accessible strategies for teaching mathematics. Numerous geometric concepts, including shapes, symmetry, and transformations (like slides, flips, and turns), can be effectively illustrated through engaging art projects, providing an enjoyable and educational experience. Additionally, consider harnessing art projects as a creative means to teach concepts such as measurement, ratios, and arrays, which relate to multiplication and division.
11. Seek to develop understanding
Effective mathematics education extends beyond rote memorization of formulas and procedures, as memorization alone does not cultivate true comprehension. To foster a robust foundation in math, establish ambitious objectives, encourage exploration, and collaborate with students in their learning journey. Delise Andrews suggests treating students as budding mathematicians, where you introduce a broad topic, explore various problem-solving strategies, and then prompt the students to derive a formula or idea themselves, rather than starting with the formula. This approach nurtures a deeper conceptual understanding and forges stronger mental connections between students and the material.
12. Give students time to reflect
At times, educators become so entangled in meeting curriculum demands and the pressure to cover all the material that they inadvertently neglect to provide students with the opportunity for reflection on their learning. To address this, students should be encouraged to engage in reflective practices. This can be done through written reflections at the conclusion of an assignment or lesson, facilitated through class or small group discussions, or conducted via teacher-student interviews.
Allowing students the time and space to contemplate and articulate the significance of what they’ve learned, identify areas of remaining uncertainty, and express their curiosity about further exploration is of paramount importance. This not only furnishes valuable insights for teachers but also empowers students to self-monitor their progress and adopt strategic thinking in their approach to mathematics.
13. Allow for productive struggle
When presenting students with an authentic problem, it’s beneficial to pose a substantial question and encourage them to grapple with multiple approaches to resolve it, according to Delise Andrews’ suggestion. She emphasizes that as a teacher, your role is to keep the learning engaging by posing the right questions at the appropriate junctures. This approach ensures that you don’t stifle their thought processes but rather facilitate their progress toward a solution.
Minimize the amount of information provided while ensuring it is sufficient for students to be productive. Effective mathematics instruction involves supporting students as they wrestle with mathematical concepts and interrelationships. Allow them the freedom to explore what works and acknowledge setbacks along the way, fostering a growth mindset in their approach to mathematics.
14. Emphasize hands-on learning
Math often involves abstract concepts, but a valuable strategy to make these ideas more tangible is hands-on learning. Whenever feasible, integrate math manipulatives into your teaching approach. For instance, you can employ LEGO bricks as a versatile tool to impart various math skills, such as grasping concepts related to area and perimeter and enhancing comprehension of multiplication.
15. Build excitement by rewarding progress
Students, particularly those who may have struggled with math in the past, can sometimes harbor negative attitudes towards the subject. To counter this, contemplate implementing a rewards system where students can earn points and receive certificates, stickers, badges, or trophies as they make progress in their mathematical journey. Additionally, consider organizing weekly announcements and assemblies to celebrate the achievements of top-performing students and teams, as this can be incredibly motivating.
As Sarah Bax points out, having these moments of recognition is profoundly influential. With consistent practice and motivation, students can witness their improvement over time, building excitement and allowing one of the most effective strategies in teaching mathematics to thrive.
16. Choose meaningful tasks
Engaging children in mathematics becomes much more exciting when they tackle real-life problems. For instance, when instructing sixth graders on calculating area, consider assigning tasks connected to a house renovation, as recommended by Fennell. Provide them with wall dimensions and window sizes, and challenge them to figure out the remaining space for wallpaper. Alternatively, ask them to calculate the number of tiles required to cover a deck. It’s entirely feasible to introduce problem-based learning, even within a virtual learning environment.
17. Play math games
Maintaining student engagement and active participation can prove challenging, particularly when the curriculum heavily relies on worksheets. Incorporating games, such as those designed for first-grade math, offers an exceptional means to infuse enjoyment into learning while concurrently enhancing strategic mathematical thinking, computational fluency, and comprehension of mathematical operations. Games are particularly effective for kinesthetic learners and also strengthen the connection between home and school when they are provided for additional practice at home.
18. Set up effective math routines
Students tend to exude confidence and competence in the classroom when they understand both what they are expected to do and the underlying purpose of their actions. Implementing consistent routines in your math class and teaching students how to navigate them can greatly enhance the efficiency, effectiveness, and overall enjoyment of math lessons.
For instance, beginning your class with a number sense routine can set a positive tone. Productive small-group math discussions that yield valuable insights don’t occur spontaneously; thus, it’s essential for students to be well-versed in the “rules of the road” for participating, including contributing their ideas and offering constructive critiques of their peers’ thoughts in a respectful manner.
19. Encourage teacher teamwork and reflection
Effective teaching doesn’t happen in isolation. Collaborating with fellow educators is instrumental in enhancing your math instruction skills. Commence this collaborative effort by engaging in discussions about the objectives for the math lesson and envisaging its ideal implementation. As a team, devise plans that incorporate the most potent math strategies for achieving those goals.
Delise Andrews recommends collectively pondering the various tasks and potential student responses you might encounter during the lesson. Post-lesson, engage in reflective discussions to discern what worked well and what didn’t, thereby facilitating continuous improvement in your teaching practice.
20. Move!
While it may seem unconventional, incorporating movement and physical activity into your instructional approach can be a highly effective math strategy. Encouraging students to leave their seats can significantly boost their motivation and overall interest in the subject. For instance, you can have students:
- Form angles using their arms.
- Organize a square dance illustrating various types of patterns.
- Conduct a shape scavenger hunt within the classroom.
- Incorporate periodic runs or other exercises and graph the results.
The potential applications of these strategies in teaching mathematics are virtually limitless, limited only by your creativity and the specific math concepts you intend to teach. For more active math game ideas, you can explore additional resources.
21. Be a lifelong learner
In general, students tend to develop enthusiasm for a subject when their teacher exudes passion for it. Yet, fostering excitement for teaching math can be a challenge if your own understanding of the subject has remained static since your elementary school days.
For instance, if you’re teaching the division of fractions by fractions and your comprehension is confined to simply following the “invert and multiply” rule, invest time in comprehending why this rule is effective and how it translates into real-world applications. Once you’ve cultivated confidence in your own mathematical proficiency, you can then impart math lessons with assurance and enthusiasm, effectively employing teaching strategies that resonate with students.
