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Student Mastery: How Will I Know When They Get It?


You’ve seen it all through the Math-U-See curriculum: “Make sure your student has demonstrated mastery before moving on.”

How do you know if your student has achieved mastery?

How Do You Know if Your Student Has Achieved Mastery?

How do you know if he’s really grasped the concepts of the lesson? There are many ways to monitor a student’s progress to determine whether mastery has been achieved. Strategies such as informal conversations, observations, projects, and real-life experiences elicit evidence of how well a student has mastered a particular concept or skill. A key component to any of these methods is to recognize that assessing mastery is an ongoing process, as opposed to just a final test or evaluation (Tweet this).

As parents and instructors, we continuously collect information about how a student is learning and interpreting information. Simultaneously, a student is constantly informing us through his questions, explanations, and written assignments. His body language and behavior tell us about his curiosity, enthusiasm, dislike, or confusion regarding his level of comfort with a particular subject or skill. These informal observations provide opportunities for instruction to be adjusted according to a student’s needs. It also gives the student the ability to admit what he didn’t understand and openly seek help. When he is shown an alternate method, is given more time to practice, allowed a break, or simply offered the time to ask more questions, he will strengthen his understanding and progress toward mastery.

The conversations we have with students are also powerful tools for assessing mastery (Tweet this). When we listen to a student explain or “teach back” an idea or skill, we can gain a better sense of his progress. Through these conversations, we can provide descriptive and constructive feedback to help him improve his work and understanding. These conversations should avoid comparisons with other students and be specific, timely, and encouraging to help clarify any misunderstandings of the topic or skill. Asking questions that are focused on the task, rather than the student, can help foster confidence and reassurance. For example, questions such as, “Can you tell me more about that?”, “How would you set up this word problem?”, or “How did you arrive at your answer?” all invite a student to share and extend his thinking by requiring him to provide a clear explanation. In these moments we have the unique opportunity to reteach, refine, and help a student improve his understanding toward mastery. The role of proficiency is also an important consideration in the mastery process. A student who has demonstrated a conceptual understanding but has not yet become proficient (in terms of automaticity) will eventually begin to struggle as he moves forward. For example, the inefficiency of a student who understands the concept of multiplication but has not committed basic facts to memory will impact future learning.

Long-term projects and real-life applications can encourage students to take responsibility for their own learning and successfully progress toward mastery. As we are directing our child’s education, we should take care that we have a good understanding of what concepts are needed for the project so that unrealistic expectations do not result in frustration on the part of the student. Projects such as making a kite, creating a board game, cooking, woodworking, caring for animals, or raising a garden can provide deeper understanding of already-learned concepts and can serve to introduce new concepts. In these instances, valuing and monitoring the steps and processes that are taken toward developing the final product are essential for a student to move toward mastery. While engaged in the project or task, a student may seek suggestions to improve or clarify information or skills. For example, a student who is working to create a sled kite may ask for support or validation of his methods when he is realizes he has to divide the width into equal fourths and the height into equal thirds. These moments of inquiry can be used to modify the activity or guide instruction to help the student achieve mastery.

It is important to keep in mind that all students are unique and, therefore, mastery may take a few days or a few months. Keep the focus on how a student learns best. Listen, observe, and provide meaningful feedback to help the student improve at his own pace. It is important to monitor and adjust instruction through observations and conversations at each stage of the learning process. Mastery requires practice, re-teaching, encouragement, and patience. When a student can enjoy and benefit from the journey of practice, he will learn to persevere during the learning process and achieve mastery.

Proponents of math mastery believe that math is learned best when learned incrementally, with one skill building on the next.




About Scottie Altland

Scottie Altland is a certified elementary educator with specialties in math and curriculum development. Previously, Scottie taught grades 5-8 in public schools and worked for a local non-profit organization, offering families and students a broad range of family life education programs. As a mother of two, she enjoys spending time with her family, is an outdoor enthusiast, and continues to love teaching and learning. For the past year, Scottie has served as the Elementary Math Editor for Demme Learning.


  • Carrie Gutwein

    My nine year old went through Primer and Alpha before we switched to a different math program last year due to frustration over the mastery aspect. We spent 2 years on Alpha because he couldn’t seem to master the math facts. Now he has reverted back to using his fingers to do math facts he new two years ago. I love MUS but the mastery aspect didn’t seem to work for him. He has been working on adding and subtracting 4 digit numbers with borrowing and carrying. He can do it but takes a while because of using his fingers and gets overwhelmed by the big numbers. I think I have a harder time teaching him because math comes easy to me and I enjoy it, but must not be a good math teacher. He has been using Xtramath.org since October and is still working on his addition facts.

    • DemmeLearning

      Hello Carrie,

      Thank you for your comment.

      I am sorry your student became frustrated with math. Your message sounded like his main trouble was in memorizing facts.

      Remember mastery and memorizing (proficiency) are different skills. When a student has mastered a concept he fully understands it well enough to teach it back to you. One way to measure this is by having him work 3-4 problems telling you the steps and you asking questions. If he is successful, then he has mastered the concept.

      Memorizing facts is the step after mastery. This is usually a lot more difficult than understanding the concept and requires the facts to be stored in long-term memory. It also takes more time.

      Using the steps “Build it, Write it, Say it” with the Manipulative Blocks will assist him in moving the facts to long-term memory. Then he will have more confidence and less frustration when working larger problems.

      Please call Customer Service as we would like to support you and your student. We are available at 888-854-6284 between 9:00 am and 6:00 pm EST.