The Assessment in Education: Assessment of Mathematics Learning

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Introduction

Today’s Learning and teaching are increasingly becoming characterized by assessments, which act as effective tools for making data-driven decisions. An assessment plan is an essential tool, not only used to measure the performance and progress of individual students but also to plan for more steps in Learning and teaching improvement. It also helps in sharing relevant information with all the relevant stakeholders involved in the learning process. This paper will consider Assessment based on various theoretical perspectives with a comprehensive description of how the plan will be used towards the Assessment of mathematics learning, for Learning, or as Learning.

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Some of the key highlights will include the use of formative evaluation for instruction, the developing of both performance and critical thinking-based Assessments, and a dissemination and implementation plan. The plan will also detail the methodologies of sharing grades with both students and parents. This is in addition to the philosophy of Assessment used by a particular school; a way through it will be shared with parents and other administrators, as well as two rubrics. A PowerPoint presentation that summarizes the main points of the Assessment will be developed at the end.

Assessment of Learning, For Learning or As Learning

This plan will combine the Assessment of Learning, for Learning, and as Learning. The Assessment of Learning will be done at the end of a learning activity and will be aimed at offering achievement evidence to parents, students, and educators. The vision of this exercise is to ensure that Assessment is fully integrated into the process of Learning. For this classroom assessment, the teacher will play the central role and act as a mentor, a guide, an accountant, a reporter, and a program director. As a mentor, the teacher will offer support and feedback to each learner (Suskie, 2018). As a guide, the teacher collects diagnostic information that aids in leading learning groups throughout the learning session.

As an accountant, the teacher is charged with the responsibility of maintaining the achievement and progress of students’ records. Additionally, they also report to the student, parents, and the school administration the achievement and progress of the student.

Finally, as a program director, the teacher makes various revisions and adjustments to instructional practices. The Assessment of Learning is a summative approach primarily intended to certify Learning and report the progress of the student to parents and the student himself. This will be generally characterized by comparing the relative position of the student vis a vis other learners. Since this assessment plan will be classroom-based, the Assessment of Learning will be conducted at the end of each course, unit, and program. It will be carried out in the form of exams or tests that will be drawn from the materials studied in class within a specified school calendar.

The teacher will use the exams and tests to assess the student’s accuracy and quantity of work. The teacher will then mark the exams and grade the students accordingly. This Assessment will put a lot of emphasis on comparing students. The grades or marks obtained from the tests and exams will form the feedback. From this approach, the teacher will be able to tell which students are either doing well or poorly in math. By extension, the teacher will also be able to identify the broad range of mathematics knowledge and skills that have been conceptualized by his students (Syaifuddin, 2020). Besides, by ranking students in order of performance, the teacher will know which student to place in what group during group work sessions. However, this assessment type seems to be simplistic and limited in scope. Therefore, the plan will also entail an Assessment for Learning.

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The traditional school assessment perspective of Assessment of Learning will be supplemented by the Assessment for Learning. Through this, more emphasis will now be put on formative Assessments rather than summative Assessments. Here, the teacher will gather a plethora of data to be used towards the modification of students’ learning works. Mathematics assessment tasks that reveal more information about what students know and do will be created. This will be expected to produce insights to be used for designing the next steps in worksheets, student-teacher conferences, observation, and classroom questioning. Any other means necessary for the provision of more information will be utilized in teaching and planning.

Although marking will also be a useful tool in the Assessment for Learning approach, it will not be for purposes of comparing the academic performances of learners but rather highlighting their strengths and weaknesses. This will aid in providing feedback that will be used in furthering the learning process. Additionally, the role of the teacher will entail using his personal knowledge of his students and how they comprehend the curriculum targets and assessment contexts to detect specific learning needs. As opposed to the Assessment of Learning that will be conducted at the end of Learning, the Assessment for Learning will take place during Learning. This learning approach will be expected to be more interactive, where teachers provide and offer feedback to learners. Assessment for Learning will rely on the diagnostic skills of individual teachers.

The two approaches discussed above place the teacher at the focal point of Learning. However, the formative Assessment cannot be complete without the input of the learner. The student also plays an important role in the learning and assessment process, in addition to being the key linkage between the two. The Assessment as a learning approach, therefore, recognizes the student as the connector of learning and assessment processes. If students are actively engaged as critical assessors, they will be able to make good sense of information, master the math skills and relate them to knowledge acquired before (Siagan et al., 2019). The ultimate goal of an Assessment as Learning approach will be to empower students to monitor what they are personally learning. The feedback that they will obtain will be used for the necessary adaptations and assessments as well as significant changes in what they comprehend.

Towards this end, the Assessment as Learning approach will seek to allow the students to bring out their knowledge and talents in a self-motivating fashion. Further, students will be expected to bear the problems and decisions they commit in their lives without relying on the teacher or any other person to tell them whether an answer is right or wrong. Assessment as a learning approach is an effective assessment approach that will be expected to empower students to explore different acting and learning strategies as well as ask reflective questions. With time, the students will be expected to acquire relevant strategies that will propel their Learning to use their knowledge in constructing meaning (Chizhik & Chizhik, 2018). This is in addition to possession of self-monitoring skills that will make them discover if they do not understand something. The three assessment approaches discussed above will be formative evaluation processes of the student in this learning approach.

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Implementation and Dissemination

Assessment of the performances of students should be a constant cycle that identifies areas of improvement. Every session of learning is an ongoing data collection process. This student assessment plan will seek to achieve four objectives. First, it will provide a precise conceptualization of the targeted learning outcomes of the student. Second, it will describe the methodologies to be used in assessing and measuring the outcomes. Third, it will describe the results that have been attained from the measures (Tucker et al., 2020). Finally, the assessment will describe how the current practices are validated and point out areas that need to be improved or changed to enhance student learning.

The first thing to do in the implementation process is to establish if the assessment plan offers the answers to what exactly the students should do and know and how they should achieve this. After the implementation of the assessment plan, it is significant that the teacher analyzes the results obtained to identify the areas of improvement and change. Implementation is preceded by having in place a proper structure that will ensure the sustenance of the program. Since this is a mathematics class, there will be a Mathematics Departmental Assessment and Implementation Committee. This department will be charged with the responsibility of sharing expertise, interests, and knowledge in the assessment process.

The implementation process of this assessment plan will take place in four steps. The first step is to precisely identify and define the learning outcomes. At least five learning outcomes will be formulated, followed by a description of the student’s abilities, knowledge as well as attitudes, and values at the end of the term (Suurtamm et al., 2016). The intended learning outcomes for this mathematics class at the end of the term are as follows;

  1. be able to effectively communicate mathematical ideas,
  2. use mathematics to solve problems in unclear settings,
  3. demonstrate the significance of mathematical concepts in daily life,
  4. produce and interpolate graphs of different functions,
  5. use graphs and algebra to solve inequalities and equations.

The second step will be to select the most appropriate measures of assessment and assessing the learning outcomes. Specifically, direct measures of learning will be used to assess the learning outcomes. In this measure, rubrics will be used to describe and assess the students’ performance levels. Results of the three assessment learning approaches will form the data, which will then be aggregated and analyzed for different students. Efforts will be made to ensure that each student’s confidentiality is protected (Duchesne & McMaugh, 2019). For this specific math class, the learning outcomes will be assessed through performance assessment, short investigations, open-response questions, portfolios, self-assessment, and multiple-choice questions.

Performance assessment will be achieved by giving the students complex mathematical problems to solve both individually and as a team. In those teams, they will learn to apply separate knowledge grains and brainstorm together through collaborative efforts aimed at solving problems together. In short investigations, students will be provided with basic math problems to solve. By so doing, the teacher will know whether the said student has mastered the basic mathematics skills and concepts taught in class.

Meanwhile, the open-response questions are where the teacher will ask the students their understanding of the real world to establish how they can put their analytical processes into practice. This can be through a drawing, a brief oral or written answer, a chart, a diagram, or a graph, and a mathematical solution. 15-minute assessments will be conducted during the term to test the students’ comprehension of the broader world (Bump, 2018). Throughout the term, student’s improvement and progress as they learn new concepts will be documented in such portfolios as group reports, peer reviews, student outlines, and notes, journal writing, as well as diagrams and artwork.

After every math topic, the teacher will ask the students to identify the most difficult sub-topic, what approach the student thought could have been used, if they could do it differently, and the lessons are drawn. These are self-assessment questions that will help individual students assess themselves. Although multiple-choice questions are not true reflections of student assessment in a mathematics class, they can help reveal the student’s understanding of various mathematical concepts as well as the student’s ability to integrate these concepts into their daily lives.

After identifying these learning outcomes, the teacher will embark on the analysis of the same. The primary objective of each of the learning outcomes will be to ensure that the student moves from point A to B as a learner. This will be established through observing the student’s ability to extrapolate real-world problems using mathematical concepts. It will not depend on rubrics, grades, and scores alone (Gutierez, 2016). Therefore, the teacher will allow the students to self-evaluate themselves in addition to interviewing them on an individual basis.

The final implementation step will be to carry on relevant adjustment measures in tune with the assessed learning outcomes. Indeed, the assessment results can only make sense if they are used for the purposes they were intended for (Morris & Hiebert, 2017). Therefore, this is a crucial implementation stage; otherwise, the whole assessment process would have failed. Some of the adjustment approaches will include restructuring teaching methods, assessing the learning approaches in use, employing the reversed learning model, adopting new technology, and carrying outdoor classes.

The results of assessments should encourage restructured teaching aimed at improving the student’s grades and sharpen their academic prowess. For instance, if one approach will be found not to generate the required results, a new one will be embraced. In this case, individualistic tests might be turned into group brainstorming sessions. It is expected that the revamped model of teaching will grab the students’ attention and improve outcomes (Stahnke et al., 2016). Indeed, when a significant learning process is changed, it inevitably inspires drive among learners. Some of the learning methods that will be considered include flipped learning, microlearning, mastery learning, and blended learning.

The teacher will also be encouraged to pay closer attention to students’ learning processes by inviting them to participate in open talks where they will be able to expose their strengths and weaknesses. This way, the teacher will be in a better position to establish and fix what needs to be corrected. Sometimes a student might be suffering from fear, anxiety, or lack of confidence, which significantly impacts his learning process. This can only be determined through an open discussion with the teacher.

The reversed learning model is characterized by changing roles in class. In this model, the student becomes the teacher and vice versa. In a math class, students can be bored with the teacher since it requires the presence of the teacher daily in class. To make learning more friendly, the students will be encouraged to assume the role of the teacher. Additionally, the teacher will explore various technologies to aid in teaching (Backfisch et al., 2020). There are many online platforms such as Udemy that contain vital contents that the teacher can leverage on. This will inspire the students to take a more active role in learning and hold discussions with their classmates regarding what they will be learning.

The teacher will occasionally decamp from traditional classroom teaching and take students somewhere else in the open where they can speak freely. Teaching in an environment where students do not feel that they are contained can produce marvelous results. Such open places as parks and fields may instill in students a sense of freedom, which can, in turn, change the way they perceive different mathematical concepts. All these will be implementation procedures that will be aimed at establishing the efficacy of the learning assessment plans.

Sharing Grades with Students and Parents

One of the most effective ways of engaging parents in improving the school’s academic performance is to share assessment results with parents. Indeed, parents need to know how their children will be assessed in school. The use of report cards and test reports has been the most traditional one. However, this method does not appropriately share assessment parents with students and parents. Although there are several ways, both formal and informal, that teachers can use to share assessment data with parents, it will be important to follow established communication protocols (Kim & Bolger, 2017). These will include face-to-face meetings, written communication, and digital communication.

Face-to-face meetings will be carried out with parents at the beginning of the term to explain to them the goals of the assessment and what is expected of the students at the end of the term. During this meeting, the teacher and the school administrator will share with the parent crucial details of the assessment and its relevant policies, as well as explain assessment feedback and activities (Gotwals & Birmingham, 2016). This will help pacify any frustrations that might arise from parents, such as getting concerned about the amount of homework given to their children.

The assessment plan is cognizant of the fact that not all parents will manage to attend these face-to-face meetings consistently. Parents unable to attend the meetings will be communicated with through written texts. The school will send out curriculum topic sheets and newsletters to such parents. These will be expected to communicate to the parents what their children are studying and will be assessed on.

The newsletters will be sent in regular intervals and will be expected to maintain contact with them in addition to encouraging them to get more involved with the education of their children. However, the reports will only carry minimum information that will be consistent with what parents need (Lindvall, 2017). They will not be expected to burden teachers in their preparations. Useful assessment information that outlines the strengths and weaknesses of the child will be given the utmost priority.

A grading system of attitude and achievement will be used to avoid lengthy reporting. This will be accompanied by the written section that offers information on specific strengths and weaknesses instead of generalized remarks. This will be a self-assessment by students directed to their parents for comments. It is expected that the reports be produced early in the term to allow parents ample time to follow up and perhaps contribute to pointing out areas of development (Kennedy, 2016). Assessment information to parents will also be shared through emails, e-newsletters, digital apps, web portals, and other digital messaging systems. This will be expected to reduce the risks of printed reports disappearing.

The School’s Philosophy of Assessment

The philosophy of assessment of the school will be developed under four precepts; teaching and learning, measurement, compliance, and reporting as well as student-centered. Under the teaching and learning principle, an assessment will be considered as part of student and pedagogy erudition inspired by subject questions regarding programmatic and classroom practices intended at guiding future developments in both learning and teaching (Ulandari et al., 2019). Therefore, this assessment will be formative in nature and purposed at enhancing the teaching and learning of mathematics as a subject. Assessment will thus be viewed as a learning process within the program.

The principle of measurement denotes the determination of reliable and valid approaches to the collection of data to student learning to drive discussions and decisions on the assessment of the same. The philosophy will thus be to determine and measure the most accurate and appropriate procedures of recording and documenting learning and its institutional and programmatic impacts. Some of the measurement issues will include longitudinal data, controls, and comparisons (Guzey et al., 2017). The philosophy of assessment under compliance and reporting is to meet the demands and requirements of such external entities as the school administrators, parents, and state agencies.

The assessment principle of student-centeredness operates under the philosophy of allowing students to take charge of their own learning initiatives by actively participating in the assessment process. This means that assessment is used as an engaging and reflective process that enables students not only to learn about themselves but also what and how they learn. Thus, the students are not just assessment objects but agents of it.

Sharing the School’s Philosophy of Assessment with Parents and Other Administrators

Parents and other school administrators play an important role in learning assessments and must thus be involved in the entire process. Sharing the assessment plans with them will hence enhance their involvement in the growth of the students. The teacher will encourage frequent meetings with parents and administrators to communicate the plans. In such meetings, they will suggest to the parents and administrators the kind of activities that should be done to improve their understanding of the process. It will be important for the parents to be informed about allocating a quiet and comfortable space at home, away from digital distractions where their children can study (Short, 2017). The teacher will also remind the parents and the administrators of the significance of assessing the students.

The process of assessment will begin with the basics of bettering parents’ comprehension. This will enhance communication between the teacher and the parents and administrators. Hence, the teacher will commence by explaining the objective of the assessment process and its different approaches. Moreover, the teacher will also share with the parents the assessment tests that will be applied and the expected results. Whenever an assessment will be given a communication will be sent to the stakeholders. The same will apply when the assessment results will be out (Remillard & Kim, 2017). These results will indicate the learning progress of the students, and must also be shared with the parents. while on this, the teacher will be pointing out the students’ academic strengths and weaknesses and how the weaknesses can be addressed.

Rubric 1

Holistic Scale 1 2 3 4 5
Task Completion No response/blank Demonstrates minimal understanding Completion of some significant task components Completion of most key task components The student completes all key mathematical components
Communication of ideas Answer lacks clear communication Clear communication of ideas Clear communication of ideas Clear communication of ideas
Demonstration of understanding Unable to demonstrate the generation of strategy Demonstration of conceptual understanding gaps Demonstration and understanding of relevant mathematical processes and concepts In-depth demonstration and understanding of relevant mathematical processes and concepts
Processing of ideas Totally irrelevant or incorrect Misunderstands or overlooks less significant ideas Choice of more sophisticated and efficient processes where appropriate
Interpretation of ideas Provision of insightful extensions and interpretations where appropriate
Application Applications, analogies, and generalizations

Rubric 2

Holistic Scale 1 2 3 4 5 6
Fails to achieve any of the task’s requirements Non-completion of the task’s requirements Limited completion of the task’s requirements Substantially completers the task’s requirements Fully attaining the task’s requirements Solid work that surpasses the task’s requirements
Nonsensical, illegible, and irrelevant responses that do not relate to the task Fragmented comprehension of the mathematical processes and concepts of the task
Results incomplete and disorganized
Understands some mathematical processes and concepts of the task but still show visible gaps Understanding of most mathematical processes and concepts of the task Good comprehension of the mathematical processes and concepts of the task Complete understanding of the mathematical processes and tasks
No comprehension of the mathematical processes and concepts of the task Only superficial and a few task elements identified Identify some of the tasks’ significant elements but visible flaws in some element assumptions Identification of some significant elements though not all Identification of all or most of the significant elements Clearly identifies all the task’s significant parts
Lack of or unsuccessful attempt to communicate ideas Muddled, incomplete, and incoherent attempts to communicate ideas. General difficulties in communicating mathematical ideas though can attempt to express some concepts Some elements of experiments, designs, analysis, investigations, solutions, and experiments may be missing from a task Evidence of experimentation, modeling, analysis, interpretation, and investigations Concise evidence of purpose mathematics execution
No attempt to justify or explain results Illogical, circular, and convoluted attempts of justifying or explaining results Ineffective procedures analysis, inappropriate results interpretation, unclear mathematical arguments, and limited solution strategies Adequate communication but with limited variety and clarity Successful and clear communication of concepts Excellent mathematical arguments and prose
Utilization of some inappropriate techniques and tools to solve the tasks presented Occasional mathematical thinking evidence involving conjectures, predictions, comparison, generalizations, and interpretation Solution of mathematical problems and interpretation of results Thoughtfulness and creativity in communication
Limited techniques and tools used in solving problems Mathematical thinking evidence Multiple assumptions-based solutions
Application of a variety of techniques and tools towards task solutions Rare insights into the problems’ solutions
High mathematical thinking level
Exceptional skills in selecting appropriate techniques and tools for mathematical solutions

Formative Evaluation Example

One of the most appropriate examples will be to use task cards in a mathematics practice activity. Students do not normally have sufficient time to finish up all the task cards. This problem will be solved by keeping a couple of task card sets as formative assessments. The student will complete mathematical problems about their whiteboards.

Task cards for formative evaluation.
Figure 1: task cards for formative evaluation.

Recommendations for School-wide Training

  1. The assessment should be regularly administered both in the classroom and outdoor settings to monitor the individual performances of students and how they adapt to instructions
  2. A wide assortment of strategies suitable for individual student inferences should be used during assessments.
  3. The applied standard-based assessments should be tailored to initiate the targeted instructions. This means that the assessments must be aimed at detecting the impacts of high-quality learning and teaching.
  4. If successful, the results of the assessments should be used in subsequent terms and classrooms or even in other schools to rectify specific practices that hinder students’ performances.
  5. Standardized content knowledge that is non-referenced should be used as a performance indicator. Besides, this should not focus on instruction but on the entire learning and teaching.
  6. The assessment should involve a combination of multiple measures in such a way that students and schools demonstrate competencies in various approaches to different math problems. Such measures should be tuned to ensure that the instructions delivered are coherent.
  7. All assessment plans should be effectively shared with parents and school administrators
  8. Assessment processes should be spearheaded by teachers but must be student-centered.
  9. The assessment philosophy should guide all activities undertaken by the teacher in assessing the students. Whenever a conflict of opinion arises, the philosophies should provide the way forward.

Conclusion

Assessment is a fundamental part of learning and teaching in schools. It is an essential tool that provides data for measuring students’ performances and progress. While developing an assessment plan, there are different things to factor in, key among them being the subject area and the intended learning outcomes. Based on this, an assessment can either be performed as Assessment of Learning, For Learning or As Learning approaches or a combination of all. Due to the intricacies involved in mathematics learning and teaching, all the approaches are required for use. Assessment for learning and assessment of learning approaches give more power to the teacher while the assessment as learning style is more student-centered.

To implement an assessment plan, the teacher must first establish if the plan is precisely tailored to meet the students’ learning outcomes. Implementation is an ongoing cycle whereby data received from the assessment is used to inform the areas of improvement and change. This implies that the results should be used in restructuring teaching and learning for the purposes of improving the students’ academic performances.

Even though assessment plans are developed and implemented by respective teachers, it is important to involve parents in their executions. Their feedback will help the teacher to know more information about his students for closer attention. Thus, effective methods of communication should be used to share the plans with parents. Moreover, assessment plans should be guided by respective schools’ assessment philosophies. This provides uniformity and a common path for students belonging to a particular school. The same should be shared with parents and school administrators as well.

References

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Ulandari, L., Amry, Z., & Saragih, S. (2019). Development of learning materials based on realistic mathematics education approach to improve students’ mathematical problem-solving ability and self-efficacy. International Electronic Journal of Mathematics Education, 14(2), 375-383.

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