Math Resource Critiques Essay

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Mathematics: A Critique of Two Products

Jump Math

Description

Jump Math refers to an educational resource primarily to be harnessed by teachers which covers the curriculum needed for students from grades one to eight. It uses a pedagogical method referred to as "guided discovery" or "micro-investigation" which supports the student making small discoveries or steps, learning basic concepts one at a time which they can then build on. "Students learn and understand mathematical concepts by answering questions and working independently to challenges, while being strictly controlled by the teacher and receiving support at all times" (jumpmath.org). Essentially the method believes in the balance of the student engaging in exploration, with assessment and evaluation: discovery is safe because the teacher is always there to help aid discovery.

Suggestions for Use

Jump Math would be ideal for students who have severe math phobia or who have an extreme dislike for mathematics, perhaps as a result of a bad experience in math. Instead of putting the focus on results or simply "getting the right answer" Jump Math focuses on how math can be a process of discovery, which even kids who have the greatest hatred for math will come to appreciate, as nearly all kids like discovery. Furthermore, it gives these kids an important life lesson that they can use in all fields of academics -- that they don't have to complete everything all in one step, but can break off smaller, bitsy pieces. This is so crucial because many adults still have anxiety about math and feel like they haven't mastered it (Tips et al., 2010). This comes from experiences of feeling unempowered as a child.

Personal Opinion about Suitability for Grade Three

This product is ideal for the lower grades of elementary school, because it is often in these lower grades that students develop poor opinions of their ability to do math, and create a self-fulfilling prophesy that their ability to do math is not good. This can be so detrimental as it's an attitude which can follow some people through life. Furthermore, grade three students are ones which still enjoy learning through play and the fun of being inquisitive. Jump math capitalizes on these tendencies. The success of Jump Math with grade three is not simply that it's fun and encourages exploration: it helps to build confidence which the child will have with him for life.

Jump Math and National Standards

Jump Math has a great deal of overlap with the national standards of the NCTM and the overwhelming belief about mathematics teaching in Ontario Canada. Both Ontario's standards and the NCTM's standards focus upon the importance of monitoring and evaluation: "Effective assessment can have a dramatic impact on student learning. Teachers recognize that different assessment strategies generate different information, and they understand that it is important to build a repertoire of assessment strategies to use in the classroom" (Ministry of Education). Jump Math is so reflective of these standards and others because things like teacher-monitoring are built in to the structure of the program. The goals and objectives of each section and of each aspect of the yearly curriculum are addressed in an organized manner, but broken up so that students can master the concepts in small pieces, while still accomplishing the national standards in a timely fashion.

Developmental Needs of the Intended Audience

Third graders need to flex their muscle that allows them to engage in the concrete operations stage of thinking that allows them to reason logically about actual objects and organize their thoughts in a lucid manner (GCSID, 2007). Jump Math reflects these needs and does not force them to do things like engage in abstract thoughts, instead forcing them to learn through active, concrete experiences in the simulate environment provided by the product. Jump Math harnesses new abilities that children of this age group have and helps them to develop it even further: for example, Jump Math can increase their attention span, develop their problem solving abilities and help them to collect, classify and organize information (GCSID, 2007).

Product and Child Learning

The product reflects an understanding of how children learn. In most schools, children learn mathematics in a tense, strained environment which is often very stressful, and children ascribe far too much importance on their success in doing so. While their success is important, too many students feel that if they have trouble with math, it makes them "stupid." The product reflects the fact that lasting learning for children revolves around a spirit of curiosity -- when children have a real desire to figure something out and get to the bottom of things, finding an answer out for their own edification. That is truly the most remarkable aspect of Jump Math as it capitalizes on all of these things.

Gap Closing

Description

Unlike Jump Math which is more of a methodology of an approach for all students in learning certain concepts in mathematics, Gap Closing is designed particularly for students who need extra help. Whereas Jump Math is designed to be fun, Gap Closing is more scientific. "For each topic in the resource, there is a diagnostic and a set of intervention materials. Diagnostics are designed to uncover the typical problems students have with a specific topic. Each diagnostic can be used to tailor differentiated lessons as instructional decisions are being made for the struggling student" (edugains.ca). This program has a strong focus on doing math that is grade appropriate and a constant act of assessing and evaluating the student to ensure that the approach is being harnessed properly by the student.

Suggestions for Use

The best use of this product would be for the struggling student who needs to get caught up to speed on the concepts and benchmarks of mathematics for grade three. The goals of Gap closing are so clear and so precise, that it truly benefits the remedial student or the student who struggles with mastering concepts and other tasks. Gap closing is so ideal because it can be used for independent learning or for collaborative learning. It's also ideal because it allows the teacher to continue monitoring the student and helps with the assessment of objectives and how well the student is mastering material. Gap closing is designed so that any weaknesses in understanding are immediately uncovered. This can assist the teacher greatly, and show the teacher what she could spend more time on.

Personal Opinion

My personal opinion about the potential effectiveness of gap closing is very low. I find that the methods and materials primarily used in this product are very unoriginal and don't differ wildly from the bulk of educational materials already on the market for students in mathematics. It essentially appears that Gap Closing is made up of worksheets which are tailored to specific mathematical abilities and levels of comprehension of the student. While the program does use pictures and diagrams a great deal throughout the materials -- which will be incredibly helpful to the grade three student and a lot of learners who find certain mathematical concepts hard to grasp -- there's very little that's innovative. Essentially the product believes in teaching students math by providing them with more work and lots of it.

Gap Closing and National Goals for Student Education

Gap Closing does reflect many of the national goals for student education in the province of Ontario and by the nation of Canada as a whole. Because Gap Closing focuses so strongly on the just the numbers and the importance of learning concepts, regardless of whether or not the experience is fun for the child, Gap Closing has a tremendous amount of overlap between the goals of the nation in regards to the mathematical ability and learning of their students. Gap Closing orbits around collecting data (student results) and evaluating it, something that is a tremendous part of the national standards: "By gathering and analyzing student assessment data and other relevant information (e.g., observational notes, anecdotal records), teachers and administrators ensure that their improvement strategies are based on a correct understanding of students' levels of achievement" (Ministry of Education). Gap Closing thrives on such ideologies, basing the entirety of the learning materials on creating work for students to complete and for teachers to evaluate.

Gap Closing and the Development Needs of the Student

Some of the developmental needs of the grade three student are addressed by Gap Closing. For example, students in grade three need to practice engaging logical reading, increasing their attention span, using reason and rationale, organizing and classifying materials and other goals. Gap Closing addresses these necessities in an indirect manner; instead Gap Closing focuses on the mathematical concepts that these students need to be able to master. These mathematical concepts and problems require that the student be able to do things like reason, concentrate and solve problems.

More than anything, Gap Closing focuses on the individual curriculum goals for grade three, such as number sense and numeration, fractions, measurement, geometry and spatial sense, patterning and algebra, data management… [END OF PREVIEW]

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