The “math superstars” displayed conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. According to Suh (2007), conceptual understanding is grasping mathematical concepts. Procedural fluency refers to how well students can use these concepts in practice. The ability to answer mathematical problems fast and accurately is a good indicator of strategic competence. According to Suh (2007), adaptive reasoning necessitates applying logic, while productive disposition reflects and explains the usage of the process in the context of a given circumstance.

According to Suh (2007), procedural fluency plays a dominant role in defining mathematical proficiency in many traditional classrooms. Procedural fluency in numbers is critical to students’ comprehension of place value and rational numbers. Comparing and contrasting different ways of tackling mathematical problems is also essential. As well as relying on written instructions, these strategies include mental approaches to calculating specific sums and differences, as well as those that use calculators and computers.

According to Suh’s (2007) reading of Lesh et al.’s translation model, students make more meaningful connections when representing a mathematical idea in verbal symbolism, manipulatives, written symbols, real-world context, and visual models. For instance, Lesh et al.’s paradigm has textual symbols, vocal symbols, real-world events and pictorial representations, and tactile graphics. Therefore, Suh (2007) believes that this model may allow for a more effective connection by expanding this paradigm to include moving pictures.

Manipulatives are not effective for describing and justifying various mathematical procedures, such as compact algorithms. Subsequently, students would not have a more profound knowledge of mathematical reasoning when prompted to use manipulatives to describe and examine their results.

To help the students know if mathematics is sensible, the author allowed them to use whatever resources they had accessible to them as models. In Suh’s (2007) opinion, all children should start problem-solving skills at three years. For this reason, the author did everything she could to supply a wide range of manipulatives to meet the needs of different tasks and procedures. Children can also explore the strength and potential of a specific manipulative during specific lessons, which may be helpful for them.

Problem-solving is one of the four arithmetic proficiencies that the author refers to when discussing children’s ability to study and solve real-world situations using the “Convince Me” activity. It is one thing to know what makes an excellent instructional exercise; quite another to put that knowledge into practice while working with students. Having a basic understanding of classroom standards is another way to establish and implement them to a varied student group.

Suh (2007) had a thorough understanding of the subject matter she was teaching and the broader context she was coaching. The author noticed that the students’ results and their knowledge of their mathematics had improved in school. She also saw that teacher content expertise and student achievement improved performance. As a teacher, one needs to know what they want their students to learn and measure their progress in that particular subject. Educators need flexible knowledge to review and modify educational materials present information understandably while also assessing what students are learning. According to Suh (2007), teachers need to hear and see students’ mathematical concepts. This learning includes understanding how children’s mathematical concepts develop over time and determining where a child may be on that path.

## Reference

Suh, J. M. (2007). Tying it all together: Classroom practices that promote mathematical proficiency for all students. *Teaching Children Mathematics*, *14*(3), 163-169.