A Review of General Strategy Instruction and Schema Based Instruction in Solving Mathematical Base Word Problems.
Problem solving within mathematics is important as children need to apply and transfer their learning of how to solve calculations into everyday situations. Enabling children to deduce what algorithm is required in a given situation is important as the way in which a problem is approached (NCTM, 1989) is an essential skill, in addition to arriving at a correct answer. Furthermore the NCTM (1980) recognised that teaching problem solving to children develops their skills and knowledge that are used in everyday life whereby the inquiring mind, tenacity and receptiveness to problems are developed.
One area of problem solving is word problems which Jonassen (2003) summarises in his research that “Story problems are the most common kind of problem encountered by students in formal education.” (p. 294). Given that word problems are the most frequently visited type of problem solving the type of instruction and modelling of approaching and solving word problems must be carefully considered and as Haylock (2010) comments the teachers need to “… focus on children’s graspof the logical structure of situations…” (p. 95).
A review of the literature associated with solving mathematical based word problems showed a vast array of research examining the instruction of how to approach and solve word problems. In particular two different approaches to problem solving; general based instruction (GSI) and schema-based instruction (SBI).
GSI uses metacognitive and cognitive processes. Pólya (1957) details in his book How to Solve it, four principles in approaching a given problem (i. understand the problem, ii. devise a plan, iii. carr...
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... the students had not answered the problem as they had focused on the numbers provided and not what was asked and Dickson, Brown and Gibson (1995) comment that students must be enabled to “… transfer problems into their symbolic representation…” (p. 361) so as to help them approach more difficult problems with the appropriate algorithm.
The fourth stage requires reflection (Pólya, 1957) checking the calculation (Rich, 1960) and verification (Garofalo and Lester, 1985). The fourth stage is where the student needs to reflect on all three previous stages and that their conjectures in the first two stages were realised in the third stage. In addition students need to demonstrate that the computations used in stage three can be applied to problems of a similar nature. Potentially students may use “Proof by exhaustion [and] deductive reasoning”, (Haylock, 2006, p. 322.
Whenever learning about this project for SMED 310, I wanted to pick out a learner who I knew had a low self-concept and low self-efficacy in their mathematics ability. After thinking back over the years, I remembered a friend I had in high school who had struggled with their math courses. Matthew Embry, a freshman at Western Kentucky University, is looking to major in Sports Management. Whenever I was a senior in high school, we played on the same sports team. Throughout my senior year, I helped him with his Algebra 1 class. When I would help him after a practice, I could tell he struggled with the material. As a mathematics major, I have taken numerous math courses. By teaching him a lesson dealing with football, Matthew was able
Problem-solving is determined when children use trial-and-error to work out problems. The ability to consistently figure out a problem in a logical and analytical way emerges. While children in elementary school years mostly used inductive reasoning, designing general conclusions from particular experiences and definite certainty, adolescents become experienced in deductive reasoning, in which they draw distinct conclusions from hypothetical concepts using logic. This capability comes from their ability to think hypothetically. However, studies has shown that not all individuals in all cultures reach formal operations, and most of the population do not use precise procedures in all forms of their
Reys, R., Lindquist, M. Lambdin, D., Smith, N., and Suydam, M. (2001). Helping Children Learn Mathematics. New York: John Wiley & Sons, Inc.
All children learn differently and teachers, especially those who teach mathematics, have to accommodate for all children’s different capacities for learning information. When teaching mathematics, a teacher has to be able to use various methods of presenting the information in order to help the students understand the concepts they are being taught.
During baseline, the student attempted to solve four word problems, resulting in two word problems solved correctly and two word problems solved incorrectly. The student applied one step out of five possible steps when solving. Word problem sessions (1-4) for the baseline are as follows: 0%, 0%, 20%, and 20%. The baseline data showed a range of 0% to 20% with a median of 10%.
Garnett’s paper she outlines common vocabulary practices, such as defining words in the dictionary and studying root words, which have not been successful in helping struggling students. Her teaching philosophy is that vocabulary instruction cannot be a repetitious practice, but it must be flexible when working with the needs of students. Dr. Garnett’s unique and creative teaching approach caters to struggling students, such as Anthony. Her perseverance and commitment to Anthony’s education resonated with me throughout the article. She showed me that as an educator you have a commitment to your students by bringing instruction to life in the classroom, which was demonstrated in her interaction with Anthony. Kate Garnett is a role model for teachers by redefining direct instruction through effective teaching practices, such as her vocabulary game. As stated in the article “ I went home and designed a game activity with meteor, meteorite, atmosphere, friction, impact, and crater aimed at activating the verbal rehearsal so uncommon to Anthony’s repertoire (7).” Dr Garnett created games and designed activities, which would assist in the expansion of Anthony’s mental lexicon, such as category example relationships. In the article is that Dr. Garnett shares a similar approach to teaching vocabulary as with Dr. Connor and the Stahls. They are shattering common practice and giving teachers a model which will assist them when working with struggling
Although adequately developed, there are significant inconsistencies primarily between her math facts fluency and all others. She can adequately solve mathematical problems ranging from simple addition to complex calculus, demonstrating her ability to apply mathematical knowledge to complete mathematical computations. Notably, she was able to solve problems involving simple addition, subtraction, and multiplication. As the math problems become more difficult, she was less automatic primarily with multiplication and division problems. She is also able to analyze and solve practical math problems presented verbally, demonstrating the ability to apply quantitative reasoning and acquired mathematical knowledge. However, her ability to solve simple fundamental problems using addition, subtraction, and multiplication while under time constraints is significantly more developed. Overall, London’s mathematical fluency, problem-solving, and reasoning skills demonstrate an adequate mathematical
Problem solving. Within society, people are constantly solving problems whether it’s simple or complex; and young preschooler are not exempted. Thought their problems during this time may seem mediocre to adults but children do have this issue and are exceptionally better at solving these problem because of their willingness. Children can be taught problem-solving skills during the regular course of each day through modeling, coaching and adult assistance. Before beginning a problem-solving process, it is important for the child to know that there is a problem. This is easily accomplished by a nearby adult who states the fact, “I see you have a problem’. According to the Vanderbilt Center for the Social Emotional Foundations for Early Learning (CSEFEL) four steps identified for young children to effectively solve problems:
The learning objective/goal for the re-engagement lesson I designed is that students will be able to correctly identify the tens and one’s place, borrow a ten, and correctly add it to the ones place as a ten to regroup. The state content standard for this learning objective is MGSE2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. In the re-engagement lesson, I will be reviewing how to identify the place value of numbers using a ten and ones chart. We will also go over the steps to solve a subtraction problem with regrouping. Then we will review how to use base ten blocks to solve some subtraction with regrouping problems together.
Children can enhance their understanding of difficult addition and subtraction problems, when they learn to recognize how the combination of two or more numbers demonstrate a total (Fuson, Clements, & Beckmann, 2011). As students advance from Kindergarten through second grade they learn various strategies to solve addition and subtraction problems. The methods can be summarize into three distinctive categories called count all, count on, and recompose (Fuson, Clements, & Beckmann, 2011). The strategies vary faintly in simplicity and application. I will demonstrate how students can apply the count all, count on, and recompose strategies to solve addition and subtraction problems involving many levels of difficulty.
Solving problems is a particular art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice…if you wish to learn swimming you have to go in the water, and if you wish to become a problem solver you have to solve problems. -Mathematical Discovery
Breaking down tasks into smaller, easier steps can be an effective way to teach a classroom of students with a variety of skills and needs. In breaking down the learning process, it allows students to learn at equal pace. This technique can also act as a helpful method for the teacher to analyze and understand the varying needs of the students in the classroom. When teaching or introducing a new math lesson, a teacher might first use the most basic aspects of the lesson to begin the teaching process (i.e. teach stu...
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
Much current work involves identifying the cognitive components (such as memory and attention span) used in problem-solving activities. Researchers also are trying to identify the processes that occur in the transition from one level of thought to the next. Another area of investigation is the cognitive components in reading and arithmetic. It is hoped that this research will lead to improved methods of teaching academic skills and more effective remedial teaching.
...nd dynamic changes in the competitive nature of the job market, it is evident to myself that being eloquent in all aspects of numeracy tools and knowledge is imperative in the 21st Century. The calculator is one such tool for children which supports mental computation to check answers to develop independent learning, as discussed earlier. It also fits into the pre-operation developmental stage of a child to enhance their symbolic thinking, similar to that of an adults scheme of thinking, as opposed reliance on senses alone. The interviews further grounded my reasoning around my argument and allowed me to not only gain an insight to how those similar to me think and those not so similar. This investigation has strengthened my argument that the use of calculators in the primary school classroom, if used appropriately, are an invaluable tool for teaching and learning.