Students are more confident in math when they know their facts well. For example, automatic knowledge of multiplication tables takes the sting out of learning new math concepts.
Kinesthetic learners can benefit from hands-on math practice at all ages. This involves using concrete resources along with pictorial representations.
Mastering Math Facts
A child who has memorized addition and subtraction math facts can do arithmetic more quickly. Moreover, they can use their critical thinking skills to solve real math problems creatively. On the other hand, a child who can’t recall basic arithmetic facts has to think twice about each step in problem-solving. This wastes valuable bandwidth that should be saved for higher functions. These students often feel exhausted with math early on and believe they aren’t good at it because they have to spend so much energy trying to figure out basic arithmetic facts.
Practicing daily and attending or concentrating in the math department is essential to build fluency. Try using timed tests (e.g., mad minutes) to assess a student’s progress toward mastery. However, these types of tests give limited information about what strategies a student used. They also send a message to students that fast is best, which can be discouraging for slower learners. Instead of timed tests, consider doing a “math running record” or a “math interview.” Both assessments provide more data about how a student approaches a task and are more appropriate for assessing a student’s fluency.
Another great way to build math fact fluency is using flash cards. These are a no-fuss way to practice adding and subtracting, multiplying and dividing. They can be shuffled and studied by groups or individuals, and they can help visually and tactile learners commit math facts to memory.
Developing Mathematical Reasoning
Developing students’ reasoning skills can help them make sense of math. They can use reasoning to explain their thinking, support their conclusions, infer and justify solutions, adapt learning from one context to another, and apply mathematical knowledge to real-life situations.
While this reasoning can be taught, it develops naturally with plenty of experience. Just as kids need to practice throwing and catching a ball before they have excellent hand-eye coordination, they need to practice the logic of multiplication and division before they can master those skills.
Teaching for mastery provides an opportunity to give children that experience, helping them build a strong foundation in these fundamental concepts. This strategy also requires teachers to understand that not all students will simultaneously reach the same level of understanding. Therefore, teachers must allow students to spend the time they need on each concept rather than moving them on before fully grasping it.
A key part of a mastery learning approach involves careful pre-planned assessments that can weed out misconceptions before a new topic is introduced. It also consists of revisiting the same concept in several ways to reinforce and deepen understanding. These practices and a focus on building students’ problem-solving and reasoning abilities can address the widespread misperception that math is too tricky and useless in real life.
Using Multiple Strategies to Solve Problems
A key component of math mastery is helping learners use various problem-solving strategies. It’s essential to teach mental math strategies as well as more formal ones such as “guess and check” or using the technique of drawing a picture to help with calculation (e.g., a rough circle with two marks will do for chickens, while a blob plus four marks will do for pigs). These strategies allow children to develop confidence and understanding of basic number facts.
The teaching for mastery approach also helps students to understand that many mathematical concepts are connected. This is important because it recognizes that pupils will struggle to grasp more advanced topics if they don’t have the necessary foundation knowledge to support them. For example, teaching times tables to a child who needs help to grasp entirely addition is very difficult.
This requires teachers to plan lessons carefully and ensure all learners understand the basic concepts before moving on to new material. Teachers should also track individual pupil progress towards mastery, and this may mean that a few learners take longer to master the subject than others. But teachers mustn’t give up on these learners, as they may need much time to master maths.
Developing Mathematical Sense-Making
Developing mathematical sense-making involves making connections between math concepts. This can be done through examining and interpreting equations, solving problems in new contexts, and constructing and explaining reasoning and justifications. This is an essential strategy for students to develop since mathematical equations often express scientific ideas. Students who understand these equations can better solve novel or more complex problems.
A teacher can support students in this sense-making by providing frequent opportunities to practice new concepts and review previous skills. This can be done through routine formative assessment and a more intentional approach to homework that allows students to work at their level of mastery.
The order in which teachers introduce topics can significantly impact the depth of learning. Cobbling together free lessons from the internet rarely achieves a coherent order, and students may need help understanding how one lesson connects to the next.
A mastery approach allows students to take time with each topic, and teachers only move on once all students fully understand the concept. Teaching this way takes a lot of time, but it is worth the investment to help all learners reach their math potential. Teaching for mastery also recognizes that struggling doesn’t define a learner and instead provides an opportunity to fix misconceptions as they arise.
