Essay Example on Manipulatives and Visual Models in the Classroom
Manipulatives can provide a bridge between the concrete and abstract levels of many mathematical topics (Jones, 2017). This statement shows that using manipulatives effectively enables the teacher to connect the topics to the learners. So what exactly are manipulatives? TeacherVision (2007) describes manipulatives as tools designed for hands-on learning in the classroom. They can be used for the introduction of topics as well as for practicing them. Different manipulatives can be incorporated into the 4 different modes of representation in maths. This is because each manipulative is designed for use under one of the representations. This essay explores a variety of viewpoints on manipulatives and visual models in the classroom. It investigates how counters and numberlines can help illustrate the structures and laws of addition and whether using manipulatives has a impact on childrens learning.
Many teachers like to make their maths lessons engaging and fun. Which incorporates discussion into their lessons. As a result, the learners will begin to understand a variety of techniques that can be used to find the answer. Moyer (2001, p. 186) states children thrive when manipulatives are used in the classroom because they are both fun and engaging. Additionally, she mentions how she was able to observe a huge change in how active the children became during the lessons when manipulatives were used, since they needed to figure out the answer physically in front of them.
Despite manipulatives improving interactivity, there is the danger of them distracting children. Sutton and Krueger (2009, p. 91) suggest that some children may only learn about the manipulative and not the maths that is being showcased. The teacher must work with the student to ensure they demonstrate the manipulative aspect of presenting the mathematics in the question.
Special Educational Needs children can also be helped by manipulatives. The reason is that using a concrete model such as counters will enable them to repetitively manipulate the manipulative to solve each question. Lowe (2016) suggests that using a range of manipulatives and visual models will provide these learners with a different experience, allowing them to use for example numberlines for counting and money for everyday scenarios.
However, a possible limitation could be if the teacher introduces the manipulative or visual model to the children too suddenly and expects it to immediately work. Manipulatives are models which need time to be understood which is why it is imperative especially with SEN children to introduce these models as early as possible.
In conclusion, the benefits of using representations in the classroom far outweigh their limitations. This indicates that they should be used more frequently in classrooms. The introduction to them should be as soon as the child begins school, particularly with SEN children or children who struggle with maths. By blending manipulatives and visual models, the representations reveal a different way to answer maths questions. For that reason, the different viewpoints showcase how manipulatives and visual models can have a positive impact on children and their learning.
The purpose of this paragraph is to explore the addition operation further. It will showcase an understanding of the different structures and laws of addition and will also look into how the addition operation develops across the curriculum. Twinkl (2021) points out that out of the four operations, addition is the first one children learn. Addition is the operation that we use the most in our daily lives, since it is most commonly used to add two or more whole numbers together. Therefore, it was an easy decision to explore this operation.
There are two addition structures, augmentation and aggregation, but how are they different? Haylock and Manning (2019, p. 92-93) assert that both structures are basically the same in terms of their structure but differ in the style of questions they ask. Aggregation is the process of combining two numbers to make one answer. This can be taught in a range of contexts like money or in the form of different amounts of objects. To find the answer, learners will have to group the objects using concrete models, which then leads directly into having to count all the objects represented in the question.
NCETM (2021) explains that the augmentation structure is when a question starts with a certain number, and it asks the learners to add a certain amount. In order to demonstrate this structure, the teacher can ask a question more relevant to everyday life like age, money or temperature change. By doing so, the learners would see how the two structures differ. For instance, augmentation focuses solely on the terms increasing and counting-on.
There are 2 laws which are associated with addition. There is the commutative law of addition which states that swapping numbers around will still give the same answer. This is a foundational principle in the addition operation and it is critical for teachers to demonstrate this in addition calculations. The second law is known as the associative law. Haylock and Manning (2019, p. 109) explain that the associative law, like the first law, is a fundamental part of addition, but it is constructed differently using the formula a+(b+c)=(a+b)+c. It will be clear to the learner where to start the addition from via the brackets. Regardless of the order in which the numbers are placed in the formula, the answer will always be the same.
How do you eat an elephant? Askew (2015, p. 34) uses this phrase when discussing how schools split up the maths curriculum, his answer was one slice at a time. This relates directly to how the addition operation is developed across the curriculum. In each year group, the addition operation is covered. This includes learning the basics in reception all the way to calculating 3–4-digit numbers in year 6. By using concrete and visual models in reception, children will understand what the manipulatives represent and can use this knowledge when it comes to answering questions in year 6.
To conclude, this paragraph shows an understanding of the addition operation by showing how the structures and laws are taught throughout the childrens time in school.
Teachers use counters for math activities in the classroom very often as they are very easy to work with. This means that if a child gets the physical model wrong, they are easily able to restart and have another go. Numberlines is a visual model which is used in schools for addition and counting. Since it is a very basic model, children can use it to quickly check or answer their calculations. Photos will be used to illustrate how counters and numberlines can be used to reveal the structures and laws of addition along with demonstrating how they can be used together.
Below are annotated images of how the representations can be used to expose the structures and laws of addition in lessons.
According to NRICH (2013) counters and numberlines can be linked easily. This is due to them both being used for the same purpose which is addition and counting. Both representations can be used in all the examples discussed above. This can be done by using one of the representations to answer a question whilst double-checking your answer by using the other. Below is a sample question that links both representations together in 1 question.
Summarising all the paragraphs, it becomes clear that representations impact childrens learning. This is because they can be applied to expose all the structures and laws of addition. Teachers benefit greatly when manipulatives and visual models are linked together since they can demonstrate two different ways to work out questions. In my experience of using representations on placement, I have seen how they can help children who are struggling, as well as push others to answer increasingly difficult questions. As a result, I will definitely use representations when I become a teacher, since seeing first-hand how crucial they are in developing a learners understanding makes me believe that they are an essential resource.
