Introduction
In this chapter two, the concept of place value, the causes of learners’ inability to understand it have been explained. What authors and other researchers say are also included as this pieces is a literature reviews. A continuation of Introduction to Understanding Place Value. Continue reading.
This chapter encompasses review of the related literature. It presents review of authors, opinions of experts and media both empirical and theoretical perspective on this field of study to offer support and credibility to the current work.
The following sub-headings were discussed; learners inability to comprehend the concept of place value, teaching approaches to enhance the understanding of the concept of place value, and the use of multi-base block to enhance understand of the concept of place value.
Causes of learners Inability to Comprehend the concept of Place Value involving Addition of two-digit numbers
Learners Inability To Comprehend The Concept Of Place
Joe (2001) explained that computational weakness is one of the challenges children encounter in mathematics.
Many students, despite a good understanding of Mathematics concepts, are inconsistent to computing. They make errors because they misread signs or carry numbers incorrectly or may not write numerals clearly enough or in the correct column.
These students often struggle especially in primary school, where basic computation and right answers or stressed.
He continued that difficulties transferring knowledge is also a challenge.
One fairly common difficulties experience by people with Mathematics problem is the inability to easily connect the abstract or conceptual aspect of Mathematics with reality. Understanding what symbols represent in the physical world is important to how well and how easily a child will remember a concept.
Holding and inspecting an equilateral triangle, for example, will be much more meaningful to a child than simply being told that the triangle is equilateral because it has three equal sizes. Children with this problem find connections such as these painstaking at best (Roland, 2008).
Debbie (2007) is of the view that incomplete understanding of the language of Mathematics, for some students, mathematics disability is driven by problems with language. These children may also experience difficulty with reading, writing and speaking.
However their language problem is confounded by the inherently difficult terminology.
Some of which they hear nowhere outside of the mathematics classroom. These students have difficulty understanding written or verbal directions or explanations and find word problems especially difficult to translate.
According to (Esteen,2008:59) students’ “difficulty to comprehend the visual and spatial aspects and perceptual difficulties”, is also a problem.
A far less common problem and probably the most severe is the ability to effectively visualize mathematics concepts. Learners who have this problem may be unable to judge the relative size among three dissimilar objects.
This order had obvious disadvantages, as it requires that a learner rely almost entirely on rote memorization of verbal or written descriptions of mathematics concepts that most people take for granted.
Some Mathematical problems also require learners to combine higher-order cognition with perceptual skills, for instance, to determine what shape will result when a complex 3-D figure is rotated.
Mathematics disorder, formerly called development-arithmetic disorder, dyscalculia is a learning disorder in which a person’s Mathematical ability is substantially below the level normally expected based on his or her age, intelligence, life experiences, and educational background.
Some of the causes of these deficiencies include; difficulty in reading and writing number, difficulty in aligning numbers in order to do calculations, inability to perform calculations, and inability to comprehend word problems(Betty, 2002).
Baroody (2001) elaborated strongly by saying from reading the research, and from talking with elementary school arithmetic teachers, he suspected that children have a difficult time learning place-value because most elementary school teachers (as most adults in general, including those who research the effectiveness of student understanding of place-value) do not understand it conceptually and do not present it in a way that children can understand it.
He continued that elementary school teachers can generally understand enough about place-value to teach most children enough to eventually be able to work with it; but they don’t often understand place-value conceptually and logically sufficiently to help children understand it conceptually and logically very well.
This even impede learning by confusing children in ways they need not have; e.g., trying to make arbitrary conventions seem matters of logic, so children squander much intellectual capital seeking to understand what has nothing to be understood.
A further problem in teaching is that because teachers, such as the algebra teachers referred to above, tend not to ferret out of children what the children specifically don’t understand, teachers, even when they do understand what they are teaching, don’t always understand what students are learning and not learning.
There are at least two aspects to good teaching: (1) knowing the subject sufficiently well, and (2) being able to find out what the students are thinking as they try to learn the subject, in order to be the most helpful in facilitating learning. It is difficult to know how to help when one doesn’t know what, if anything, is wrong(Baroody,2001).
Spendilove (2009) said that inability to grasp the differences between such operations as addition and subtraction is also a cause. These symptoms must be evaluated in light of the person’s age, intelligence, educational experience, exposure to Mathematics learning activities, and general cultural and life experiences.
Mathematical symptoms include the inability to count and memorize arithmetical data as the multiplication tables. Attention symptoms are also related to failures in copying numbers and ignoring operational signs. Sometimes these failures are the results of a person’s carelessness.
Learner-Centered Approach That Enhance The Understanding Of Learners In The Concept Of Place Value
Demonstration Method Of Teaching Mathematics To Children
According to Charles (2003) demonstration is the method teaching in which the teacher displays certain objects and action in the class to teach a particular concept. This helps the learners to observe and practice what the teacher has with or without coaching.
Demonstration method comes in two types that is Method demonstration and Result demonstration.
Brookfield and Preskill (2018) explained that demonstration are essential to create a learner- centered environment that stimulate active learning, inquiry and collaboration.
The authors further argued that demonstration can be used to facilitate the development of cognitive and meta-cognitive skills by engaging students in reflective thinking and problem solving.
Research has also shown that demonstration can enhance student engagement and motivation (Felder & Brent, 2003).
When students are given an opportunity to observe what the facilitator demonstrates, they become more invested in the learning process and are encouraged to take ownership of their education through practicing what they have seen.
Demonstration can also help students develop communication and interpersonal skills, which are critical for success in both academic and professional settings.(Hoban, Giegling, Hall, Hopper, Marshall, Pinto- Basto, Portscher, Zai & Owen, 2017).
Brookfield and Preskill (2016) stated that demonstration can help learners develop critical thinking skills, build their confidence in expressing their opinions, and increase their engagement with the subject matter.
A study conducted by Bransford, Franks, Morris and Stein (1986), the researchers found that demonstration can help learners connect new information to their prior knowledge and develop more complex and nuanced understanding of the subject matter.
The authors recommended that instructors can enhance the effectiveness of demonstration by using a variety of prompts, such as case studies or problems, and by providing learners with opportunities to apply their new knowledge in real- world contexts.
Rao (2019) agrees that demonstration can help mathematical learners develop their understanding of a concept by providing opportunities for learners to practice what have been demonstrated to make their own meaning.
He proposed that demonstration can be particularly effective when they are structured on specific learning objectives with learners clear guidance in participation.
Lee (2017) highlighted that, demonstration can be an effective way to promote learners’ critical thinking and reasoning skills when learning place value.He advocated that, demonstration can be used to minimize abstractness of a lesson hence tailors easy comprehension by learners.
In summary, the literature suggested that demonstration can be an effective teaching technique for improving learners’ understanding.
This can be achieve by providing learners with opportunities to practice based on what they have observed from the demonstrating material to reflect on their understanding on the subject matter under study.
How Multi-base Block Enhances Understanding of Learners of Concept of Place Value
The Use of Multi-Base Block to Enhance Understanding
Dienes multi-based block resources provide a special model to teach place value at the basic schools. The smallest units that measure 1 cm on a side are called cubes.
The rods, narrow blocks that measure 10 cm by 1 cm by 1 cm are called longs. The flat, square blocks that measure 10 cm by 10 cm by 1 cm are called flats. The largest blocks available, cubes that measure 10 cm on all sides, are called blocks.
When working with base ten place value experiences, the researcher commonly use the cubes to represent ones, the long to represent tens, the flat to represent hundreds, and the block to represent thousands.
Providing names based on the shape rather than the value allows for the pieces to be renamed when necessary. For example, when studying decimals, a class can use the flat to represent a unit and establish the value of the other pieces from there.
Dienes multi-Based block resources are especially useful in providing students with ways to physically represent the concepts of place value in addition, subtraction, multiplication, and division of whole numbers (Dienes,2009).
To build number combinations in base ten, by using Dienes multi-based blocks, students ease into the concept of regrouping, or trading, and are able to see the logical development of each operation. The blocks provide a visual foundation and understanding of the algorithms children use when doing paper-and-pencil computation (Wheeler,2008).
Dienes multi-based block resources are used as a practical learner-centred minds-on and hands on innovative method of teaching especially difficult concepts in mathematics. He devised this approach to demystify the learning of mathematical concepts especially by the youth.
The researcher believes that the teaching of mathematical concepts should be approach through physical or practical means so that child’s mind is taken from mere association to complete generalization there by easing out abstractness found in mathematics.
Wheeler (2008) stated that multi-base block (MAB) are found in many primary school and are commonly used in teaching the presentation of place value and operations with whole numbers.
To use them to represent decimals, students need to be convinced that blocks do not always have the same value. For example, the large cube may represent (1) one rather than (1000) thousand. Multi-base block can then be used in teaching in representation of an operation with decimal numbers.
Activities such as making and naming numbers, ordering by size, estimation, addition, subtraction, multiplication, and division (as repeated addition and subtraction) in the new decimal number, ream can be given a concrete embodiment. This assist in avoiding just giving list of rules for dealing with decimals (Dienes ,2009).
Summary of the Chapter
This comprises the learners’ lack of understanding in the concept of place value, teaching strategies to enhance ability of learners, and the effect of using multi-based blocks to teach place value.
Authors like Wheeler (2008), Resnick and Ford (2001), Kercood (2004),etc spoke about the,the use of multi-based block to enhance learners’ understanding, teaching strategies to enable understanding, and learners’ lack of understanding in place value respectively.
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