Math Performance Assessment: Investigating, Designing, and Reflecting - Essay Sample

Introduction

Mathematical evaluation is of considerable significance because it enables learners to develop their thinking power, communication, problem-solving, and the linking of mathematics concepts to various applicable situations. There is a need for the changing of mathematics learning in tandem. The work aims at investigating, designing, and reflecting on the known equations and is a practical application.

Is your time best spent reading someone else’s essay? Get a 100% original essay FROM A CERTIFIED WRITER!

Save 25%

Investigate

National Standards and Best Practices in Performance Assessment

The state standards and practices in performance evaluation for mathematics ideas involve understanding problems and perseverance in solving them. The mathematical practice standard describes the diversity of expertise that the mathematics instructors utilize in their learners. The best practices lie on the significance of proficiencies and processes that are core in mathematics education (Sykes, 2016). The national council of teachers of mathematics (NCTM) process standards of thinking and proof, problem-solving, representations, communication, and the connection are the first of these standards (Sykes, 2016).

The national research council report adding it up is the next thread of mathematical expertise. It entails adaptive thinking, strategic aptitude, conceptual knowledge, procedural fluency, and productive nature. The theoretical understanding involves knowledge of mathematical ideas, relations, and operations (Sykes, 2016). Again, the procedural fluency entails skills in doing procedure flexibly, efficiently, accurately, and appropriately. Furthermore, the productive disposition includes the routine inclination to reveal mathematics as useful, sensible, and worthwhile. Additionally, this is tied with one's efficacy and belief in diligence.

List of Standards

Problem-Solving

Performing a task in which the solution is unknown in advance allows learners to utilize their first acquired knowledge in the process of gaining fresh mathematics knowledge. Problems can arise from realistic applications and experiences. Analysis of the problem should be appropriate to ensure the teacher foresees the mathematical concepts. Learners should feel secure in their instruction surrounding t enhance problem-solving. Students should have the assurance that they can freely explore, share, take risks, and argue various strategies. The environment is core in ensuring they work through challenges and problems with confidence (Sykes, 2016).

Communication

The instructors should provide a serene environment where a learner can give expressions on the starting efforts to communicating their reasoning. When learners begin to do this, teachers should be patient because communicating in mathematics is not natural to learners.

Reasoning and Proof

The reasoning being a habit should give context in the development of vital mathematical concepts. Mathematics entails discovery, and therefore it enables students to explain and explore their thinking. This is why it is always good to begin learners of what they understand and then build the concept from that.

Representation

This involves informing learners to portray their mathematical concepts in various ways (Gurl et al., 2016). Realistic situations are essential to learners because they offer them something an insight into the real meaning and purpose behind the use of mathematical ideas.

Connections

This entails the mental experience that relates one thing to another, thus increasing the learners the mathematical thinking abilities. The role of an instructor is to identify the relationship between what the students share and the connection that exists among the strategies.

How Mathematical Standards and Practices Serve as Guides

The standards and best practices offer students the chance to consider several processes in mathematics because they are utilized by the proficient in mathematics. The mathematical practice standards illustrate how developing learners engage in the subject matter as they mature in the discipline. The best mathematical practice enables one to make sense of a problem and persist in finding the solution. It also guides a learner to think quantitatively and abstractly.

Again, the standards and practices help in the construction of comments and critique their reasoning (Sykes, 2016). The best practices and standards also enable one to apply their mathematical skills to solve day-to-day problems. They also allow a proficient mathematical learner to utilize proper tools in problem-solving strategically. Furthermore, it enables students to communicate with others precisely by enabling them to define during discussions and in their thinking with others.

Design

Design of a Performance Assessment

Performance assessment enables learners to portray how they result in a given solution and the explanations for the answers. This provides information concerning learners' reasoning and thinking. The evaluation reveals various levels of knowledge in mathematics content. Best practices and standards in mathematics can be utilized in designing a performance assessment (Bryan & Clegg, 2019). is through ensuring that learners demonstrate their understanding of a concept. It can be done by a joint effort that enables solving a complex problem. It is essential because it enables them to work as a team, brainstorm, and use their grains of understanding the help the whole.

Steps of the Performance Assessment

The first step of performance assessment entails the identification of the performance-based assessment goals. Next, proper course standards that are addressed in the performance assessment are chosen (Sykes, 2016). After this, there is a need to analyze and classify the learning gap, after which one is to design the scenario after brainstorming on the scenarios. The last step is the development of a learning plan where there is a need to balance between content teaching and ensuring the learners can perform the task (Gurl et al., 2016)..

Advantages of My Assessment Design

What appeals to me in this assessment plan is the fact that it ensures learners progress towards the learning objectives. The assessment is core because it motivates the students and enables them to learn. The assessment design drives instruction and learning. It also informs learners of their progress and teaching practice (Gurl et al., 2016). The assessment design also has a role in grading, which makes the student know their position. It also portrays the student's understanding of the mathematical concepts, which enhances the learning experience aspect, hence achieving proper learning results (Bryan & Clegg, 2019). Furthermore, it makes the assessment experience motivating and inspiring to learners. Additionally, it generates feedback, which ensures that the learners act on their weaknesses.

Reflect

Value of Performance Assessment to Solving Problems

The significance of performance evaluation in solving problems involves different stages. It offers conceptual knowledge of a problem (Gurl et al., 2016). Therefore, this is through the use of pictures, symbols, and diagrams to illustrate a task. One can be able to utilize all the useful information to solve the problem properly. Performance assessment is also core in ensuring that the procedural understanding is followed. It ensures that proper mathematical terms, computations, and formulas are utilized to solve an equation. It also provides that the mathematical language and concepts correctly (Gurl et al., 2016).

Again, performance assessment is vital in problem-solving strategies and skills. The alternatives are also considered in solving the problem. Solving an equation ensures that the problem-solving strategies portray appropriate reasoning and that the work is organized and precise. The performance evaluation is also crucial in communication. In this case, it ensures that the solution follows the right steps as they flow to the next (Gurl et al., 2016). It evaluates the mathematical terminologies and vocabularies. Rubrics are crucial in informing leaner's concerning the scoring techniques before working on the works. They can also be utilized in the structuring of discussions by the learners.

Conclusion

Overall, the mathematical standard depicts the student's understanding that entails practice standards. It also provides learners with an opportunity for learners to demonstrate their skills in a given concept. Performance assessment is of considerable significance because it reveals the learners' understanding of given ideas. The performance assessment is, therefore, vital in problem-solving strategies and skills.

References

Bryan, C., & Clegg, K. (Eds.). (2019). Innovative Assessment in Higher Education: A Handbook for Academic Practitioners. Routledge.

Gurl, T. J., Caraballo, L., Grey, L., Gunn, J. H., Gerwin, D., & Bembenutty, H. (2016). Professionalization, Policy, Performance Assessment, and Privatization in Mathematics. In Policy, Professionalization, Privatization, and Performance Assessment (pp. 45-64). Springer, Cham. https://link.springer.com/chapter/10.1007/978-3-319-29146-8_4

Sykes, G. (2016). Underpinnings of the Praxis® Performance Assessment for Teachers (PPAT®).