conceptual understanding
Both qualitative and quantitative patterns were assessed through the formative assessment. The formative assessment evaluated student’s conceptual understanding through a variety of mathematical problems. Questions 1,2 (A&B), 3 (A&B) and 4 ( A& B) assessed student’s ability to demonstrate conceptual understanding in mathematics relating to fractions. In question one, students had to show how to make equivalent fractions using a number line, and an area model. The quantitative patterns for question one revealed how all 22 student in the class excelled in this particular area. All of the 22 students tested got answer one correct, therefore this informs me that students grasp this concept and that the visual of an area model may have
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Students were also evaluated to understand the concept that the sum of a fraction may be decomposed into parts (or recomposed into an equal sum). Next students had to express the decomposed fraction as a multiplication equation. Lastly, students had to label and plot the decomposed equivalent fraction on a number line with jumps (representing the decomposition). These concepts which all correlate with one another was challenging and extremely difficult for 3/4th of the students within the class. Question 3 A & B are based on the concept of decomposing fractions. Data shows 16 students struggled with question 3 A and 18 students struggled with 3B. Due to the amount of students with IEP’s, 504’s, and students needing extra math support, mathematical concepts and skills are challenging and often these types of student population have gaps in learning. As stated previously 3/4ths of students, especially those students with special needs did not comprehend the concept. It is quite possible many students did not receive or understand the foundational fraction concepts and notions. The students that fall bellow grade level really required further instructional on the concepts of what a fraction is.
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
Abhi is a stage 3 student from Year 6, who recently attempted his selective school test. Having a conversation with his parents helped me to know that Abhi enjoys doing maths and is working at appropriate stage level. Abhi states that his most interesting topics in maths are place value, angles and geometry (I-04), as they are easy to understand (I-05). Whereas, he hates fractions and decimals (I-06) as he found them to be very confusing (I-07).
On tasks measuring math computation skills, Deanna was asked to solve problems using addition, subtraction, multiplication, division, fractions and algebraic equations. Deanna scored in the average range, as she was able to correctly respond to questions involving addition, subtraction, multiplication and division. Deanna noticeably struggled when solving equations involving fractions. Whether adding, subtracting, multiplying or dividing fractions, Deanna constantly got these questions wrong. In addition to this, Deanna’s lack of exposure to algebraic equations involving logarithm and exponents were noticeable as those questions were often left
Participation in external professional development, professional reading and shared professional discussion of formative assessment strategies and techniques. Development of physical resources to support the implementation of strategies.
Today, schools in Oklahoma are being graded largely on their students’ achievement levels in four core curriculum subject areas (Oklahoma State Department, 2014). If a student fails to gain the knowledge needed in only one content area each year, then by the end of 5th grade he or she could possibly be behind in six content areas or be six years behind in one area. A number of students come into (6th grade) middle school math classes without the necessary math skills to begin the state core curriculum for their grade level (O’Byrne, Securro, Jones, Cadle, 2006 ). Oklahoma’s 6th grade math curriculum has definite expectations that must be met before a student can begin the curriculum and expect to have any success. Students entering 6th grade are expected to be proficient in operations with fractions and decimals (Oklahoma Academic Standards, 2014). During sixth grade students will learn to evaluate expressions and solve equations that contain fractions and decimals (Oklahoma Academic Standards, 2014). A need exists to find the best method to identify the students with deficiencies and address those deficiencies by adjusting instructional strategies at the beginning of the school year in order to give those students an opportunity to be successful in class and to score at the proficient level on state tests.
Nine out of 14 students in the “Minions” and “Mickey Mouse Clubs” played this game effectively, demonstrating positive growth. While a few students needed some assistance, and were not able to do it completely independently. Students in the “Looney Toons” and “Peanuts” continue to struggle a bit with this, but they were able to show they could refer back their notes and work with a partner to solve the division problems. Many students in these groups chose to use the partial quotients strategy or the picture model. This may be because they are bit more visual for these concrete learners. These strategies also relate to skills we have been working on in previous units for place value and multiplication. Overall, only about half of the students were able to show full mastery of these concepts, and a majority of them were in the upper level tiered groups which was a bit expected as they are able to grasp concepts a bit quicker. Students in the lower level tiered groups are still continuing to make wonderful positive growth, but have not demonstrated full mastery of the third
The national curriculum (2013) highlights the importance of conceptual understanding in mathematics which will be explored though this essay. Ofsted (2012:6) support this by stating that ‘the responsibility of mathematics educations is to enable all pupils to develop conceptual understanding of the mathematics they learn. This will be explored by considering the use of cognitive dissonance in mathematics and promoting relationships between schemas. This will be further developed by analysing a mathematics lesson on fractions where cognitive dissonance was caused to promote conceptual understanding. It will begin by defining conceptual understanding using the work of different theorists.
...). Understanding the concepts of proportion and ratio among grade nine students in Malaysia. International Journal of Mathematical Education in Science and Technology, Volume 31, Number 4, 1 July 2000, pp. 579-599(21)
The article "Formative Assessment Made Easy: Templates for Collecting Daily Data in Inclusive Classrooms," explores the use of three types of formative assessment strategies: an anecdotal seating chart, daily scorecard, and an objectives grid. The opening scenario in the article describes the frustration of a special education teacher, in an inclusive classroom, who is grading her students' work and notices that they all performed poorly on a summative assignment. As this teacher thinks back to where the students went wrong, the text differentiates between formative and summative assessment.
Students continue to struggle to understand rational numbers. We need a system for identifying students’ strengths and weaknesses dealing with rational numbers in order to jump the hurdles that impede instruction. We need a model for describing learning behavior related to rational numbers – prerequisite skills and development of rational number sense – that is dynamic and allows for continuous growth and change. It would inform us of the important background knowledge that students bring with them and the prior experiences that influence their level of understanding. It would further enable us to assess students’ current levels of understanding in order to prescribe the necessary instruction to continue forward progress. Designing a method for assessing students’ conceptual understanding of rational numbers that has this potential is a challenge. In this paper, I will discuss where the call for conceptual understanding stems from in the recent past, what has already been done involving assessment of conceptual understanding, what reach has revealed about acquiring skill and number sense with rational numbers, and describe a plan using this information for developing a continuum of rational number skills and concepts.
Mathematics is considered as a difficult school subject by majority of the students around the world. In a survey conducted by Gallup in 2005 as cited by Fleming (2014) in her article Why Math is Difficult, 41% of girls and 31% of boys said that mathematics is the most difficult subject. Mathematics can be difficult especially if someone lacks conceptual understanding. Likewise in mathematics education, there are issues where student teachers in math and even some math teachers have difficulty in teaching mathematics because of unpracticed and forgotten concepts, and lack of conceptual understanding in mathematics. According to Kilpatrick, J. et al. (2001), conceptual understanding,
Using a four step model for math problem solving has been successful in many ways. Each step was taught individually and then the importance of all the steps together became the next goal. As many of the students were not reading at a high enough level to independently read the problems, I continued to read the problems to the majority of the students. The children learned to underline the numbers in the problem and listen for key-words and phrases (e.g. How many in all? How many more? How many fewer?) These key phrases were an excellent way to differentiate and challenge students who had mastered the simpler problems. The simplest problems involved primarily “How many in all?” where the student was solving for the “whole” in a
The early acquisition of mathematical concepts in children is essential for their overall cognitive development. It is imperative that educators focus on theoretical views to guide and plan the development of mathematical concepts in the early years. Early math concepts involve learning skills such as matching, ordering, sorting, classifying, sequencing and patterning. The early environment offers the foundation for children to develop an interest in numbers and their concepts. Children develop and construct their own meaning of numbers through active learning rather than teacher directed instruction.
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...