Literature Review
Assessment in Mathematics
The New Zealand Curriculum [NZC], The New Zealand Curriculum Mathematics Standards for Years 1-8 and the New Zealand Number Framework form a continuum of learning progression throughout Years 1 – 8 and beyond. Deciding where a student is placed on these paradigms and the formation of effective subsequent future learning goals is bound to the use of appropriate assessment in the classroom. Effective assessment will involve and benefit students whilst supporting teaching goals; the components will be planned and communicated, suited to a specific purpose, have fairness, and hold validity in result (Ministry of Education [MOE], 2007).
Neill & Fisher (2010) state “when we assess something we want to know its value” (p.307) as pertaining to knowledge, skills, understanding, attitudes and beliefs at any given point and time in order to improve both learning and teaching. Effective assessment in mathematics involves the triangulated use of relevant summative, formative and diagnostic tools with emphasis placed on how an assessment tool is used; indicating the consideration of applicability to the learner, as apposed to which actual tool is chosen (Mills, 2015). The MOE (2015) advises the judicious use of assessment tools to locate challenges in student understanding, informs Overall Teacher Judgment and provides evidence for accountability purposes.
Summative
Summative assessment is a valid reporting tool for accountability
Getting assessments to the desirable level is therefore vital, both for teacher and students. From the Educational Assessment Landscape chart, I believe the measurements go hand-in-hand to offer students the opportunities to show what they have learned through differentiated assessments, all leading to the final result of success in summative
I am a strong believer that one test defines a students. Therefore, variety is key when assessing students. When using formative assessment I use student reflections, journal entries, exit cards in addition to non verbal communication such as thumbs up or down. I also make anadotal notes on students to help assess the overall learning journey of the student. When using summative assessments, I use district assessments, state assessments, portfolios, short answer, multiple choice, and student based projects. In all forms of assessments, students are provided the appropriate accommodations. My learning goal for assessing students is to have a valid assessment that demonstrate the student’s understanding of the specific skill. It is crucial that I understand the purpose of the assessments and the content that is being taught, therefore, I often start instruction with the assessment piece in
Assessment, both formative and summative, plays a significant part in the learning experience as it determines progression and enables learners to demonstrate that they have achieved their desired learning outcomes.
Assessing the children understanding is considered to be a good indicator of their learning and development process (Reys et al., 2012). Stiggins (2002) discussed the difference between the children’s assessment for learning and assessment of learning. Teachers need to be familiar with both. Assessment for learning (or as we call it the formative assessment) helps the students to learn more about different concepts and increase the opportunity to develop various skills. On the other side, assessment of learning (summative assessment) is to give the teacher an evidence of students’ achievements for purposes of accountability and reporting. For example, assessment for learning can include the teacher’s observations, in-class assignments,
Assessment is a process through which we gauge a learners level and progression, ensuring learning is taking place and the learner is developing their skills and knowledge. Susan Wallace recognises the importance of assessment as more than a means of determining learner achievement but also “as an indicator of the quality of learning.” (2007: 119) discussing the need for ‘ongoing assessment’ to evaluate how receptive learners are to the lessons.
1.1 Assessment measures the learner’s progress towards or the completion of, the learning aim and criteria, and can be used at any point during the learning cycle. It can provide information to adapt the delivery to suit the learner’s needs and abilities; a learner may need more help or time on some aspects, or has progressed quicker than planned and requires additional goals. By standardising the assessment process this creates uniformity for all learners.
Assessment is an imperative part of the learning process. According to Stiggins and Chappuis (2012), “Assessment is, in part, the process of gathering evidence of student learning to inform instructional decisions. This process can be done well or poorly.” To learn more about assessment I sat down for a one on one interview with Jim Libretti. Coach Libretti is the head coach of the freshman football team at Paradise Valley High School. Also, he is a math teacher.
This October 2017, practicum observation at Sharpsville Elementary consisted of a third grade Math Assessment interview and observation. The third grade teacher works on formative and summative assessment in the math class. The teacher uses different ways to assess students in the classroom. In most cases, whether the child is above level or at the level where the child should be she has many options and strategies on how to solve mathematical problems as a whole-group or individually. This reflection will discuss the formative assessment, summative assessment, how students respond to the instruction, and a student interview observation..
Efficient educators know and understand the importance of selecting, planning, and implementing effective assessment tools and strategies that measure student’s levels of understanding. Different types of assessments are used for a broad range of purposes that include formative, placement, diagnostic, and summative assessments. However, the main purpose is to “foster learning in all its forms” (Lefrancois, 2013, Ch. 6.1). Teachers use pre, formative, and summative assessments to determine what students know before, during, and after instruction. Each measurement is used to plan, modify, and adjust instruction to meet the needs of all learners. Although each form of assessment plays a critical role in ensuring all students succeed, educators
For the majority of these classes, I must rely on my own assessments to measure my effectiveness. Using the TI-Navigator system, I formatively assess students by sending questions to solve throughout the period. I then determine whether to address the entire class or to work one on one with a student. Often students mimic the mathematical process, but have little understanding of “why” so I assign writing journals to encourage mathematical thinking. Reading the journal provides me insight into the student’s understanding, their decision making, and any misconceptions they may have to guide my future lessons. Within my classroom, I integrate a variety of hands-on activities that expand my students’ understanding of mathematics: dressing as a zombie to model exponential growth, performing “Function Aerobics” to move as the graphs shift, and measuring football lights outside using trigonometry. I always seek innovative ways to teach mathematics that is relevant to my students’
It is important to have an understanding of the mathematical concepts from years one through to three. By completing the Early Years Mathematical Competency Test [EYMCT] I was able to see my strengths and weaknesses and compare them to the Australian Curriculum Assessment Reporting Authority [ACARA]. I was then able to look at the four elements questioning, play, the on-going nature of assessment and planning for teaching and using hands-on resources and manipulatives. By comparing my EYMCT results
When planning unit outcomes, the Australian Curriculum, local context and needs of individual students are considered. This ensures relevant stakeholder interests are balanced and meaningful outcomes developed (Dowden, 2013). The Australian Curriculum, guided by the Melbourne Declaration on Educational Goals for Young Australians, outlines the official mathematics curricula to ensure students are taught the required knowledge and skills needed is consulted initially (Dowden, 2013). This is important as the Australian Curriculum has been planned with future educational and employment goals
Assessments are integral parts of instruction, they determine whether classroom goals have been achieved, and help teachers know what areas they should focus on and maybe reteach. They are great tools for developing lesson plans and answer questions such as; “do my students possess full understanding of the material?” There are many ways of assessing students’ learning, one of which I have personal experience with are on-the-spot assessments.
Informal assessment allows students to demonstrate their learning in a variety of ways which can benefit all students. It can include group or individual projects, presentations, essays, experiments, or demonstrations. Each of these can allow for “knowledge that transfers from one situation to another [which] is based on students’ abilities to understand central principles, see connections and make distinctions, and be strategic in attacking problems and analyzing information” (Darling-Hammond, p. 285). A variety of assessment methods allow for this to happen and for students to use their personal strengths to demonstrate understanding of the information. “Research into students’ preferences for alternative assessments shows that the assessments that have been positively evaluated by students were more authentic and thus made learning more realistic and powerful” (as cited in Brown, Irving, Peterson, and Hirschfeld, 2009, p. 99). Students should be able to think creatively and take hold of their own education and learning because they must ideally be prepared for a rapidly changing society where they must be able to adapt and formulate their own solutions. Teachers are able to provide feedback to the children so they know what was done effectively and what needs to be modified. Rather than teachers pressuring students to show understanding through a single examination, they will have opportunities to confidently demonstrate knowledge with less
It clearly spells out that assessment aims to point out strengths and weaknesses which then will serve as a basis in improving academic instruction and capabilities both by the students and teachers. In this same vein, this study aims to discover if more frequent assessment will result to better achievement in Mathematics.