SECTION D - gROWTH IN ASSESSMENT

Caption

The focus of this section is performance assessment, which has two general components; formulation and grading.  When formulating a task, the examiner must be cognizant of various standards of assessment, such as validity, fairness, unbiasedness and so forth.  Additionally, thought must be given to the structure of the assessment, which is dictated by factors such as learning objectives.  After an assessment is submitted, the context of grading comes to the fore.  This entry is significant as it examines the concept of assessment through a multitude of perspectives.

Growth in Assessment Competence

1. (a) Identify and explain any two standards of classroom assessment or test development with examples and reference to supporting literature.

Assessment has traditionally been used by individual teachers to monitor student learning and to provide a reference for assigning grades (Glaser & Silver, 1994).  They may take the form of tests, portfolios, presentations and so forth, are time specific and measure students’ knowledge according to guidelines specified by a curriculum.  A meaningful assessment facilitates a barometer through which students’ understanding of skills and concepts may be gauged.  They may also benefit educators, informing the teacher to modify instruction, or of the administrator to tweak curricula.  Due to their inherent importance, much planning must go into their development and implementation.  Assessment standards exist as guides for the successful construction of tests, and provide a framework for acceptable evaluation practices.  They provide a mechanism through which schools may be accountable for what students learn (Raizen, 1998), and have been embraced as a way to improve education (Weiss, 2002).  According to the Joint Committee on Standards and Education Evaluation (JCSEE), there are sixteen assessment standards which are placed into three categories; namely Foundations, Quality and Use.  Within the ‘Foundations’ and ‘Quality’ domains lie the standards of ‘Learning Expectations’ and ‘Unbiased and Fair’ respectively, which will be explicated upon in this essay.    

The Foundations domain is constructed under the premise that assessment practices are related to learning outcomes, and may be used to inform both teacher’s instruction and student learning.  Learning expectations are foundational to an assessment, as they identify which concepts and skills may be examined.  The student is then aware of key aspects of the curricula, as well as the relative importance of certain topics over others.  Thus, a student that is preparing for an exam may schedule sufficient study time on critical aspects of the assessment.  Depending on availability, suitable past papers may also be shown to students, so that they can contextualize exam difficulty and have a general outlook of assessment criteria.

 The Quality domain provides guidelines for fairness and accuracy of assessments.  Unbiased and Fair practices ensure that implementation and decision-making strategies are independent of extraneous factors not related to the assessment.  When facilitating a fair assessment, the examiner is concerned with level of mastery of material, and should not consider external factors such as student’s charisma, attitude, race, gender and so forth.  That is, a fair assessment is objective and should be untarnished from any implicit bias regarding the student’s persona.  There are a few strategies which may improve fairness and eliminate bias in a given assessment.  One such strategy is to plan and design the test in advance, carefully choosing questions that are fair to all students involved who have been studying based on the criteria of the curriculum.  This may also reduce bias which may be caused unintentionally.  For instance, a probability test based on a deck of cards, may be unfair to students who have been unexposed to card games.  Finally, a teacher may ask other colleagues for their opinions on an examination, to see if it adheres to basic standards.         

References

Glaser, R. & Silver, E. (1994).  Assessment, Testing and Instruction: Retrospect and Prospect.  In L. Darling-Hammond (Ed.), Review of Research in Education.  Washington, DC: American Educational Research Association.

Raizen, S. A. (1998).  Standards for Science Education.  Teachers College Record 100 (1), 66-121.

Weiss, I. R. (2002). Investigating the influence of standards a framework for research in Mathematics, science, and technology education. National Academy Press.

1. (b) Critique an assessment in which you have already constructed by:

    (i) assessing the extent to which it conforms to the two standards discussed in (a)

   (ii) offering suggestions for its improvement, so that it aligns with the standards discussed.

The assessment that is being sampled is for my Pure Mathematics class, at the Caribbean Advanced Proficiency Examination (CAPE) Unit I level.  The syllabus is prescribed by the Caribbean Examinations Council (CXC) and consists of three modules.  Students are graded by two external assessments, and a School-Based Assessment (SBA) worth twenty percent.  The SBA consists of three internal assessments which are delivered in class by the teacher, generally after the completion of each module. 

The exam that is being critiqued for the portfolio is a Module 2 Internal Assessment.  Within the syllabus document, both the general and the specific curriculum objectives are clearly identified.  It is based on these objectives that the assessment has been constructed.  The test shown consists of nine questions worth a total of sixty marks, including a mathematical modelling question as per the requirements of CAPE.  In this report, I am assessing the extent to which this exam conforms to the standards of learning expectations, unbiasedness and fairness.

Learning Expectations

The Foundations domain consists of ‘Learning expectations’ and five other standards which are geared towards fair, student-focused assessment practices.  The teacher that utilizes this domain sets an exam that is targeted towards pre-defined objectives and uses relevant testing strategies that may be used by an appropriate audience. The elements of these expectations will now be cross-referenced by guidelines from the JCSEE (1994) and Suskie (2018). 

· Guidelines:

Identification of all concepts and skills that students are expected to learn and demonstrate. 

Learning expectations are clearly articulated.

The assessment obeys this principle, as all of the skills that the students were expected to learn were clearly articulated in the CAPE Pure Mathematics syllabus.  I had also reinforced this information to the students, indicating that the assessment was based on Module 2 material, and that they should prepare themselves for a modelling question.  

· Guidelines:

Recognition that more emphasis may be placed on different aspects of the curriculum.

Scoring criteria are connected to learning expectations.

Prior to the test, information was conveyed to students that for the assessment, more focus should be given to trigonometry than parametric equations.  This is exhibited in the exam as seen in the distribution of marks towards trigonometry relative to parametric equations.  This emphasis is practical as well, since trigonometric questions are generally more prominent in the CAPE examinations than parametric equations.

· Guideline: Use of examples so that students are aware of learning expectations.

Students were shown previous years’ internal assessments with solutions and marking schemes.  This was done to familiarize them with the level of analyses that were required to attain full marks.

Unbiased and Fair Assessments

The Quality domain is hallmarked by the elements of dependability, inclusivity and accuracy.  The standard of ‘Unbiased and Fair’ lies within this domain, and is categorized by the need for tests and decisions to be independent of factors that are unrelated to the assessment.  According to Lam (1995), a fair assessment is one where students are granted equitable opportunities to demonstrate their knowledge.    

· Guideline: Avoidance of complex and confusing language that may assess unrelated skills.

The instructions in the assessment are clear and unambiguous, and the vocabulary used is appropriate for this level.  Students may have had issues with the mathematical jargon, but may be symptomatic of their unpreparedness for the examination.

 · Guideline: Alignment of assessment with material that is taught, and vice-versa.

Material for the assessment was extracted from Module 2 of the CAPE syllabus, and relevant principles were taught using the syllabus as a guide.  Therefore, the examination was fair as students were exposed to the curriculum content before the examination.

Suggestions for Improvement

I believe that the assessment material conformed to learning expectations.  However, due to the number of topics on the syllabus, time in class was primarily spent on delivery and completion of material, rather than on performing adequate checks regarding students’ progress.  This could be rectified by introducing a tutorial session within the teaching schedule.  Finally, although the exam was fair and unbiased, more teachers could have been asked to review the assessment for relevant checks and balances.  This may have been time consuming though, but could be accomplished in the future by setting the exam well in advance.           

References

Joint Committee on Standards for Educational Evaluation. (1994). The program evaluation standards: How to assess evaluations of educational programs (2nd ed.). Thousand Oaks, CA: Sage.

Lam, T. C. M. (1995).  Fairness in performance assessment.  ERIC digest (Online).  Available: http://ericae.net/db/edo/ED391982.htm (ERIC Document Reproduction Service No. ED 391 982)

Suskie, L. (2018). Assessing Student Learning: A Common Sense Guide (3rd ed.). Jossey-Bass.

Section D – Growth in Assessment Competence

Part 2 (a) 

The topics of Series and Sequences are included in the CSEC Additional Mathematics curriculum.  A sequence is a list of numbers placed in a particular order, the sums of which can be utilized to form series.  The understanding of sequences and series are crucial for the study of more elevated branches of Mathematics, including Calculus, Analysis, Combinatorics and so forth.  These also lend themselves to other fields that include physics, computer science, finance and engineering.  Therefore, it is quite important that this concept is introduced to budding mathematicians at the CSEC level, since it will auger well for their later academic development.  Series and sequences are covered more rigorously at the CAPE level, and this suggests that O-Level students should acquire a grasp of these concepts, as these will form requisite knowledge for A-Levels.   

For this unit, focus is given on arithmetic and geometric progressions, of which there are a few critical ideas that must be expounded upon.  An arithmetic progression is a sequence where terms are generated through addition of a constant term known as a common difference.  Students would have to understand that if they are given successive terms, then the common difference can be easily identified through subtraction.  With regards to assessment, a popular problem involves determining the value of any term within the progression, as well as the sum of a finite number of terms.

A geometric progression is similar to the arithmetic progression, but the critical concept lies with the construction of new terms, which instead vary by a multiplicative factor known as a common ratio.  Students should learn how to determine all the terms of such a progression, as well as the first term, finite sums and infinite sums, when possible.

After learning this topic, I would encourage students to appreciate the applicability of these progressions in real-life.  This may appeal to the students via the affective domain, as they may then be motivated and encouraged to truly comprehend the concepts of this unit.

For instance, the series are paramount to a branch of applied mathematics known as actuarial science, which is based on forecasting financial and other mathematical models.  The banking and insurance sector has many investment schemes which are based on series, and one who invests in a pension say, will be able to immediately forecast the total value of their contributions at retirement.      

In the assessment given, the students would be required to create a pattern using recognizable shapes, whose quantity or dimensions vary by arithmetic or geometric progression.  This should hopefully give the students an opportunity to reflect on the applicability of this concept, and will hopefully stimulate their learning through the psychomotor domain.    

Section D – Part 2 (c)

With reference to the performance assessment and rubric constructed in (b):

(i) State the purpose of the performance assessment and rubric.

(ii) Describe how the rubric and performance assessment will be used.

(iii) What insights about the concept may students gain from performing the assessment?

In the performance assessment given, students are asked to create an artistic pattern which shows variation by arithmetic progression.  The assessment will test the student’s ability to produce work that possesses both aesthetic value, as well as mathematical order and precision.  It will assess the student’s creativity, which is defined by Franken (1994) as the tendency to generate possibilities, and by Daud et al. (2012) as the ability to develop ideas based on original thinking.  This project is based on Arts Integration, which is an approach where students display conceptual knowledge through an art form, engaging through a creative process to connect with another subject area (Silverstein & Layne, 2010).  Thus, the purpose of this assessment is to provide students a channel to display their understanding of a mathematical concept through the use of art.

A rubric delineates the expectations of an assessment through a list of required subject matter, as well as descriptors associated with levels of quality and associated rewards.  It serves as a useful guide to both the teacher and student.  It may be used by the teacher to grade students’ assignments with consistency.  It also allows students to make well-informed decisions regarding the need for revisions or improvements, prior to submission (Reddy et al., 2010).  The rubric attached has therefore been constructed with the aforementioned factors in mind. 

In the performance assessment, students are required to create a piece of art using congruent objects, where the number of shapes in each row, column or diagonal vary by an arithmetic progression.  The assessment is partitioned into two components, consisting of the art-piece and a written report respectively.  In the report, the student is first required to provide descriptions of the arithmetic sequences using pertinent vocabulary such as common difference, and so forth.  Next, the student must calculate how many objects would be contained if the number of rows in the art-piece was doubled.         

The assessment awards twenty two marks for the artwork and eight marks for the written report.  The rubric is analytic and consists of five quality definitions that allocates points on a scale from zero to four.  There are five evaluation criteria, four of which are for the art-piece.  The artwork’s evaluation criteria are Creativity, Accuracy, Understanding of Guidelines and Craftsmanship.  The criteria are not all equitable, as can be seen with the Creativity component which has double weighting and carries a maximum of eight marks.  Marks for the written report will primarily be awarded on accuracy.

The psychomotor element for this project should hopefully reinforce students’ understanding of the concept of arithmetic sequences.  After performing this assessment, students should also gain an appreciation for the existence of sequences in real life.

References

Daud, A. M., Omar, J., Turiman, P., & Osman, K. (2012). Creativity in Science Education. Procedia - Social and Behavioral Sciences, 59, 467-474.

Franken R. E. (1994). Human motivation (3rd ed.). Brooks/Cole Pub.

Reddy, Y. & Andrade, Heidi. (2010).  A review of rubric use in higher education. Assessment & Evaluation in Higher Education – Assess Eval High Educ. 35. 435-448.

Silverstein L. B., & Layne S. (2010). Defining Arts Integration. Retrieved from http://www. kenndy-center.org/education/partners/defimimg_arts_integration.pdf