Various tools, AI-based aids, online platforms, etc., are available for enhancing and improving mathematical literacy. 

The processes of preaching notions of math, be it pragmatic or abstract, often lies in the hands of instructors. The students might differ when choosing the most suitable mathematical understanding and reasoning strategy. One such comparable point of Interest might be understanding procedural and conceptual math-based methods.

Some may consider mathematics to be composed of vast equations, problems, formulas, theorems, and many other extensive points of problem-solving that might make it an extensive subject of study and focus. Still, the real magic of mathematics lies in understanding the logic and reasoning behind its concepts. 

Fascinatingly, the long and complex mathematics topics might seem easy when the student gets a strong grasp of their conceptual meaning. Although procedural and conceptual math concepts may differ in some aspects, their integration and introduction from a young age help students be well-versed and increase their Mathematical literacy amazingly. 

Procedural math concept vs. Conceptual math: Comprehending the polarities

To compare the two faces of math, we may look into what each of these actually means and how handy they are. Accordingly, let’s look into each of them in detail.   

1. Procedural Math- What is it Precisely? 

The procedural math concept involves considering the rules and routines of Mathematics. Such approaches account for a series of steps that a student must follow to deal with numbers and problems. That being the case, the learner may ensure the knowledge of algorithmic skills, systematic procedures, and methods. Procedural knowledge also includes the categories used to determine when to use various steps and instructions required for problem-solving.

Here the pupils may need to rely on memorizing chapter-related specific formulae and theorems to answer questions, thereby these can be achieved even though the classroom and abstract side is compromised. These strategies may stipulate a student to use the appropriate process and undergo the required steps to achieve the answer. 

2. Procedural math- Where does it Succor?

Procedural mathematical solving works best for kids when they need to solve questions that directly involve formulas and theorems for obtaining the answer. Here, The student with gripping knowledge on principles to solve can keep up effortlessly as they apply a fixed series of step-based solving strategies. For kids and young learners, being procedural may be easy to apply. It enables the students to become more solution-oriented and lets them better focus on finding the solution with the help of a mathematical set. 

3. Conceptual Math- Why is Abstract comprehension essential?

Conceptual math often implies the awareness of concepts and techniques relevant to number literacy rather than just memorizing formulae. Comprehending the math concept implies that the student is able to grasp the  ideas behind every problem, to solve it. This ensures the strategic evaluation of numbers and not just arithmetic procedures. 

Facilitating the student to address unfamiliar challenges as well, conceptual understanding stipulates the pupil to be clear and efficient so that they mitigate the need to incline on limited knowledge. 

With additional insights, conceptual knowledge keeps the pupil ready to reason numbers, and also discern how they are fragmented and applied. Mastering the same, they can logically comprehend why an algorithm is essential and to what extent it should be considered in discerning notions. 

4. Conceptual understanding in math- Where does it come serviceable?

Conceptual learning of math integrates the functioning of ideas, this way a student can organize ideas and may later look into trying out some innovative ideas with numbers and also in solving them. This way they can focus on sorting out the problem swiftly by not completely relying on predetermined formulas and regulations. 

All this is possible as the pupil could relate facts and where these are included in math. Apart from magnifying intellect, conceptual procedures assist the individuals to discern at what time frame can a concept be actually employed in a pragmatic world. Students may require conceptual thinking in math to solve the problem logically before proceeding to the algorithmic step. 

Differences between conceptual and procedural math

Conclusion

The aspects of procedural and conceptual math are significant in many categories and elements. These techniques have their unique ways of contributing to the learning and enhancement of mathematics. They also have played a vital part in improving and upgrading various mathematical aspects, helped introduce new mathematical criteria, and developed logic and reasoning in learners.

Although many may still have different opinions on both of these topics of mathematics, the important fact that everyone needs to remember is that both of these math concepts need to be associated together to get a definite solution. They need to be also introduced and discussed widely from younger periods so that the efficiency and potential of grasping the mathematical concepts can develop from an early learning age. These concepts are crucial for enhancing and improving mathematical literacy and sense through individuals.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post Conceptual Math Vs Procedural Math: Understanding The Difference appeared first on Number Dyslexia.

Being a crucial subject to master, math often requires practice, focus, and most importantly, being well versed with its rules. Although being the elementary benchmarks of its learning, conventional mathematics rules sometimes may be pretty confusing and taxing for some learning age groups, that is, kids. 

While the journey with math may incept as with resistance, and ambiguity, practice and sequence-solving methods can ameliorate the attitude. With the introduction of conceptual learning in Mathematics, the conventional and quite familiar techniques of solving math may have taken a substantial new shift. Therefore, in this article, we will look at what exactly is conceptual-based math learning, and how can it be inculcated in the form of games and activities?

Conceptual math- Comprehending the abstract side.

In the expedition of math, pragmatic applications and concepts may often vary compared to paper-based practices. Say, a student may acknowledge that borrowing a number can lead to relevant solutions in subtraction. Nonetheless, not everyone knows the logic behind the same. Interpreting the notion and sensibilities along with procedural approaches leads to conceptual math. For that reason, Conceptual understanding of math can ensure the student decodes the schema, knowledge, composition, and arrangement of numbers. 

Such approaches to learning can be beneficial if the student ensures it from early schooling itself. Further, the implementation of manipulatives has also shown a reasonable impact in conceptualizing math. 

Nishida^[1] studied the effect of manipulatives to support children’s acquisition of abstract math concepts. The results support the belief that these can assist pupils’ understanding of math development right from elementary schooling. Further, visual math can be equally aiding. Karen C. Fuson[2] studied the combination of math words, visual images, and math symbols for understanding and competence. This research amplified Visio-spatio abilities and thereby the results showed that drawings were key visual support that helps in children transition to working meaningfully. 

Conceptual learning in mathematics: Why is it pivotal?

While focusing on procedures may be acceptable in early schooling, these practices may make the students feel arduous to grasp high-level concepts based on basic number notions. For instance, being in a professional course like engineering or accounts, composed in conceptual math may have an impact on their learning. 

Shockey^[3] studied the importance of conceptual math and its effect on children. In the report, he outlined that students can ensure precision with conceptual math, and this precision needs to continue to grow as the learner moves through arithmetic into algebra, geometry, and further mathematics. These lines show that abstract math is essential to building up core math standards. 

Grasping math often encompasses both conceptual and procedural sides, as a pupil would need to practice the notion to understand the concept. 

Classroom activities and games based on building conceptual mathematics skills

Employing games and related pedagogies may assist math skills in kids. Unfortunately, many math concepts may seek memorisation, intense practice, and repeated solving techniques to gather a good understanding. As a result, kids may tend to withdraw interest in problem-solving procedures of mathematics. Furthermore, picking higher math concepts based on these vital foundations can cause severe academic problems, making it challenging to cope later.

Classroom activities also play a significant role in building and improving the benefits of conceptual learning in mathematics. The teachers and young students create an engaging atmosphere of logic and reasoning to realize the value of an idea-based creative education system.

Here are our picks for games and activities that stipulate the conceptual side of various math notions:

1. Sort the Number cups

Learning math often starts with discerning numbers and their sequence.  While some students memorize the set of numbers, these can be conceptually retained with enticing activities. 

To start this activity, the teacher procures 10 paper cups, writes numbers from 1 to 10 on each of them, and shuffles them.  Now, the little one needs to check on all the cups and arrange them in the right sequence to finish the activity. When the learners have learned numbers, the number of cups may increase. Further, a time limit can be stipulated to make it further complex. The same activity can be mimicked to practice, even, prime and composite numbers as well. 

This activity evidently used numbers, but their sequence and magnitudes can be discerned sensibly using the sorting activities. This ensures conceptual learning when accompanied by paper-based assignments.

2. Mary’s Beads

Conceptual math can be preached by showing a real-life application of these notions. In this activity, beads in a skirt are used to practice subtraction practically.

To start with, the instructor needs to procure an outline of a skirt on a piece of paper. They can make printouts for this. In the classroom, each student is provided with a sheet with a skirt, beads, and a question. These questions are related to mary’s skirt and beads in it. The little one needs to put beads on the skirt and remove the number to find the remaining beads.

For example, If the question is: Mary’s Skirt has 6 beads, and 2 of them have been plucked out, how many beads are left out?  The learner takes 6 beads and puts on the skirt to start the answer. Now, they remove 2 beads as per the question and then count the remaining beads on the skirt (4) to answer the question. 

3. Sum these Cubes

Additions and subtractions can be learned effortlessly when any manipulations like cubes or beads are involved. This activity ensures conceptual math by letting little one discern how addition works. 

To start with, teachers offer students two sets of building cubes with two different colors along with a question written on paper.  The pupil needs to understand the questions and build up the sum with blocks to answer the query.  For instance, if the question is 5+2, the little one takes 5 blocks of one color and builds them up. Now they take 2 blocks of other colors and add them to the tower. The learner can now count the number of blocks in the tower built and write the answer on the sheet. 

4. Cake Fractions

Fractions may be confusing for little ones on paper, these complications can be resolved with a befitting activity. To start with, the mentor procures a paper cut in a circle, to demonstrate it as a cake. Now, a random fraction is explained by cutting the paper into slices. Later, each student is offered a play scissor and a circle-shaped paper along with a query. The little one needs to cut off the slice to solve the question. 

Say, the question is: the cake needs to be divided by 3 friends. The little one needs to estimate the appropriate slice size and cut them off to submit the same to the mentor. 

5. Number line fun

The number line fun activity is a beneficial and interactive learning method that helps kids understand the importance of the number line system in mathematics and solve various basic operations like addition, subtraction, etc., using its applications.

A teacher or a parent may draw a long size number line in classrooms or playing areas using chalks. The number line should be long enough to bring out the fun and theme of the game. The kids then jump from one number to another depending on the teacher’s question. For example,  if a student gets a question of solving 7+3, the teacher would tell him to walk till the seventh marking and then jump the subsequent three markings to reach the answer, i.e., 10. Similarly, the student learns about subtraction methods and other fundamental aspects of mathematics through this interactive activity.

6. Measuring the jump

Little ones are often enticed to know more about animals and birds. Accordingly, role-playing these creatures to preach numbers can turn up into an engrossing activity. 

To start with, the teacher asks the student to choose their favorite animal. Now the student needs to jump like those animals on sand so that their footmarks are evident. Now the young learner takes a tape or a scale to measure the distance between the feet, ultimately discerning pragmatic applications of numbers and measurements. For instance, if a child says that he/she likes a kangaroo, they need to jump like a kangaroo and then measure the distance between the footsteps. 

This activity is evidently marked to be assisting conceptual math skills along with being a crucial motor, and kinesthetic skill development. 

7. Buttons and the Icetray

While there are multiple procedures to make multiplications faster on paper. Nonetheless, not many of them demonstrate how these are pragmatically applicable. This activity with a button and an ice tray may turn up into a befitting multiplication activity.

To start with, the mentor procures a cup full of buttons, and an ice tray or empty egg tray along with a question. The Student needs to understand the query and apply it practically using the buttons and tray provided. Say, the question is 5*4, the student needs to put 5 buttons in each of the 4 slots of the tray. By doing this, they put a total of 20 buttons in all 4 trays.  Now, they can remove the buttons and count them to get their answer (20)

8. Compare measurement

Discerning measurement units in early schooling may not let early learners comprehend the abstract side. To ensure concept, activity may need to be implemented. Compare the limbs lets the little ones measure their limbs and compare them.  

To start with, each student needs to be ready with a scale, pencil, and paper. Now, the little one puts his/her foot on the paper and traces the outline on it. Then, they put their hand beside the previous trace and outline it with a pencil. The learner takes the scale and measures the length of their feet and compares their dimensions to comprehend how measurement is crucial. They can also compare it with their classmates the measurement of every student varies. By this activity, students can be made to understand why there are such standard units for measurement so that everyone around the world can understand and perceive the same.  Further, to make it further engrossing, they may take outlines of fingers separately and compare the difference in length among these. 

9. Pictures and shapes

Learning about shapes like triangles and squares can be interesting due to the pictorial representation of these in books. Nonetheless, these can be turned yet more enticing when the implementation of these in real life is properly discerned. 

To start this activity, the teacher procures a picture or scenery which encompasses various shapes.  Now, a copy of the same is offered to each student in the classroom. Now the pupil needs to identify and mark out asked shape out of the picture.  Say if the teacher has asked to identify squares in the picture, the learner needs to identify and mark the same with a pencil to complete the activity. 

10. Win the Candy

While most of the classroom games focus on letting the student solve the question, this game awards the little ones to identify the notion. To start with, the teacher procures a set of questions and a bowl full of candies. Now, the mentor reads out a question to the students. The pupils need to identify which math concept is to be used to solve this.  The first one who answers these queries wins a candy. 

For instance, the question is: if Ram has 5 cookies and he gives away 2 cookies to Roy, how many cookies are left with Ram? The answer here wouldn’t be 3, rather it would be “Subtraction”. 

Concluding thoughts

The fundamentals of shifting from conventional mathematical learning-based techniques to integrating them with conceptual learning innovations like pictorial representations, verbal ideas, and logical-based solution concepts have significantly improved education and subject approaches. Moreover, the association of various innovative learning procedures and strategies has been quite effective in increasing the understanding structure of subjects like mathematics, science, etc., but also has sparked a lot of interest in young learners and kids.

The primary aim of this involvement of abstract learning ideas and strategies with elementary learning methods of teaching mathematics is only to enhance the mathematical literacy of the solving procedures. In addition, these improvements have provided students with logical reasoning and thoughts that allow them more to focus on why the step was needed rather than only thinking about how they need to remember the sequence to solve a mathematical problem. 

This comprehensive learning-based system also allows kids to look and think out for innovative ideas and methods involved in tackling a mathematical problem.

References:

1. The use of manipulatives to support children’s acquisition of abstract math concepts. (2008). Nishida, Tracy Kristin.
2. Relating Math Words, Visual Images, and Math Symbols for Understanding and Competence. (2018). Karen C. Fuson. https://doi.org/10.1080/1034912X.2018.1535109
3. Uniquely Precise: Importance of Conceptual Knowledge and Mathematical Language. (2015). Shockey, Tod; Pindiprolu, Sekhar.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 10 Games And Activities For Building Skills Of Conceptual Math appeared first on Number Dyslexia.