Teaching math can feel like a large, time consuming ongoing project. It can involve whole group lessons, small groups, centers, activities and practice worksheets.
When using word problems, students need to make sense of the context and vocabulary before they can solve them. Then they can use strategies to answer the problem.
Grade-Appropriate Problems
A great way to introduce new suitable math problems is through problem-solving. Using word problems gives students a real-life connection to the math they’re learning, and it helps them build understanding of how mathematical principles apply in different situations. Word problems also allow students to practice their communication skills by verbalizing how they solved the problem. This allows them to see themselves as competent, which builds confidence.
Incorporating different types of problems in a lesson is an effective way to make it more engaging for all learners. The CRA approach, which stands for concrete, representational, abstract, offers a variety of instructional strategies to help students understand math concepts. This method starts with tangible objects, such as blocks or counters, to demonstrate a math principle, then moves to drawing pictures or diagrams to represent the concept, and finally, to abstract symbols.
As students move through the CRA process, they’re able to build on their understanding of a concept, increasing their mastery over time. Using word problems can also engage and empower students by encouraging them to use their own experiences, such as their own personal experiences with numbers or letters, to connect math to real-life situations.
Formative assessment is an important part of any math class. These assessments can help teachers identify student needs and provide the appropriate instruction to meet those needs. Often, these forms of assessment are tied to assignments that provide tiers of difficulty for students. Each tier is designed to challenge students at an appropriate level without overwhelming them. Providing this level of differentiation for students is essential to ensure they are successful in learning the content.
Another important aspect of a well-designed math curriculum is the ability to facilitate discussions between students and teachers. Discussions can take many forms, from student-led activities to guided group work. Students who are comfortable with discussing their understanding of math are more likely to succeed in the classroom.
A well-designed math curriculum also incorporates cross-curricular lessons that connect mathematics to other academic subjects, like science or social studies, to enhance the relevance of math in students’ lives. Students are more interested in math when it’s connected to a real-life situation, which allows them to use their own experiences and knowledge of the world around them as resources for solving complex problems.
Grade-Appropriate Strategies
Students need a range of effective teaching strategies in order to develop math fluency and become mathematically proficient. These strategies include the CRA approach, hands-on learning, and inquiry-based learning, among others. They also need to have access to quality curriculum and ongoing professional learning.
For example, the CRA approach (Concrete-Representation-Abstract) helps students understand math concepts by moving them through three stages. The first stage begins with tangible objects, like blocks and counters. The second involves drawing pictures to represent the problem. Finally, the abstract stage moves to traditional symbols and numbers. For example, elementary students may first solve addition problems by grouping the blocks, then drawing a picture of those groups to represent their solution (5 + 3). Teachers can further support student understanding and engagement through formative assessment practices. These involve regular, short, low-stakes assessments that allow teachers to identify students’ progress and determine the appropriate next steps in instruction.
Another strategy is to encourage students to make hypotheses about math concepts, such as “Can we use this fact when adding numbers?” This supports student agency and further deepens their engagement in the classroom. Teachers can also help students connect their learning to real-life situations by using story problems and giving students the opportunity to collaborate in small groups, constructing their understanding of a math concept together. For instance, Mathseeds offers colorful end-of-lesson books that allow students to work through math problems in small groups and justify their work as they go along.
Other important instructional techniques include allowing students to choose the number they use in solving problems, a technique known as number choice. Research shows that this helps students build a repertoire of math strategies and algorithms to be flexible in problem-solving, and that it improves their ability to answer questions that call for different strategies. Moreover, it allows students to compare the effectiveness of their chosen strategy with other strategies.
Finally, teachers should avoid excessive grading of student assignments, which can overshadow the learning goals of the assignment. Instead, they should create assignment tiers that challenge students at various levels and provide an appropriate amount of time to spend on each one. This way, students spend most of their time on the most important parts of an assignment and can practice more effectively.
Grade-Appropriate Assessments
Many assessment tools are available to help teachers assess student learning and inform instruction. These assessments range from informal (e.g., class discussions, journals, quick writes) to formal (e.g., rubrics, tests, and essays) and include both formative and summative assessment tools. For example, a teacher can use a pre-test to evaluate students’ understanding of an essential question or concept, and then conduct class discussions to gather information about how well they understood the lesson and what areas may need to be revised.
Formative assessments are low-stakes and give students valuable feedback during the learning process. They help instructors provide support that meets student needs as they move toward mastery of age-appropriate material. In addition, formative assessments can be used to identify misconceptions and false beliefs that might interfere with learning.
For example, a teacher can administer a formative assessment of students’ understanding of fractions by presenting them with a problem and asking questions about how the problem was solved. Afterward, the teacher can compare students’ responses to determine if their understanding was accurate or if they misinterpreted or manipulated the problem.
In contrast, a summative assessment provides the opportunity to evaluate student learning against the specific standards and objectives for a unit or course. Summative assessments can include graded quizzes, essays, mid-term exams, final projects, senior recitals and more. Ideally, faculty should give students early opportunities to take summative assessments so that they have time to correct misconceptions and work on misunderstandings before taking the final exam.
The Smarter Balanced assessment system and other forms of summative assessment provide educators with the ability to measure a student’s progress along the proficiency scale and see how they rank compared to their peers. These tools can also be used in conjunction with other measures of student learning, such as classroom, school and district assessments; narrative report cards; performance tasks; or informal evaluations such as class observations, presentations, Q&As and journal entries. The combination of these tools can help teachers make informed judgments about students’ learning and develop instructional strategies that best meet the students where they are.
Grade-Appropriate Materials
Many school-age students learn best through engaging, interactive lessons and hands-on activities. To reach those goals, teachers should choose materials that are both developmentally appropriate and culturally and anti-bias relevant to their student population.
In the United States, teachers largely decide what students study. Even where state boards adopt a list of curriculum materials, districts often get waivers that allow them to substitute their own choices. This results in a wide range of content and grade levels across schools. It also makes it difficult to determine whether students are gaining the foundational skills they need for future success in learning and life.
To ensure that students receive a solid core of knowledge and skill, teachers should use high-quality instructional materials (HQIM) to develop and deliver rigorous, standards-aligned curriculum. HQIM are based on research and teacher expertise, support student-centered instruction, incorporate culturally and linguistically relevant strategies and tools to help all students thrive, provide opportunities for students to productively struggle through scaffolding and rich problem-solving experiences, and have a strong focus on equity.
When selecting ELA/Literacy, mathematics, and science curriculum, educators should consider how well the materials align to state standards and the criteria for HQIM:
Gateway Criteria: Does the material fully address the standards at the level of rigor defined by the standard? Do the texts offer sufficient opportunity for all students to engage in grade-level work and develop their competencies through practice, formative, summative and authentic assessment?
Quality Reviews: Is the program subject to an independent, transparent, third-party, educator-driven review process that is designed to measure alignment and fidelity to college- and career-ready standards? Does the review panel find that the material adequately addresses the knowledge, skills and content in the curriculum?
Text Complexity: Are the student texts readable for all students? Are they sufficiently challenging for students to grow academically through the rigor of reading and discussion? Teachers’ judgments on text complexity are based on qualitative factors such as plot complexity, organization, abstractness of language and unfamiliar vocabulary, and reader/task considerations. Readability formulas are simple measures that do not take into account these factors and can be misleading.
