Curriculum, Pedagogy, and Assessment in Mathematics

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Curriculum, Pedagogy, and Assessment in Mathematics

Introduction

In teaching and assessing students, it is essential to note that various students are entitled to different ways of learning. For instance, there is the development and underpinning of the mathematical aspects of the knowledge provided in mathematics. It is necessary for teaching about the advancement of mathematical content knowledge (Dörfler, p 143 2008). The study also develops an overview of current learning theories and subsequent learning methods and the development of mathematics principles and competencies in the classroom environment by pre-service teachers (Caridade et al., p 570 2015). A variety of study viewpoints, including reading, scanning, ICT, Aboriginal and Torres Strait Islander curriculum, and special needs students, will be discussed. The planning and evaluation of learning experiences and applying frameworks to digital learning technology are given significant consideration (including handheld technologies).

Substantial resources for problems, modeling, statistical research, argumentation, and evidence are often considered (Knuth et al., p 66 2016). These areas’ historical and cultural history creates knowledge about mathematics formatting within our multicultural and global society. Focus is placed on addressing the individual differences and policies to encourage all students to think mathematically.

The evidence-based recommendation is a dynamic and multifaceted definition of learning and instruction. Although some prominent features are agreed upon, no one is described, either in the literature or by practitioners. The report encompasses cross-disciplinary areas and fields of university work, on which the organization (at its different levels) and individual academics may function (Zbiek & Larson, p 697 2015).  For the report, the evidence-based recommendations are based on Algebra for the year 7 to 10. For proper analysis and result generation, there is the creation of practical activities related to the area to cover a wide range of the knowledge content and skills within the curriculum.

Practical Activities Related to Algebra

The conception of interactions between peers is an essential part of collaborative learning. Various techniques have been applied to help students collaborate, build and retain joint awareness, such as using a concept map as a guide to show how they talk (Niaki et al., p 485 2019). The practical activities created to relate to the algebra between years 7 to 10 are listed, described, and demonstrated, indicating that the research in developing the activities is shown below.

Whole Numbers

The student explains math’s in daily languages, behavior, resources, and informal records. They also explore mathematical issues with artifacts, behavior, technology, and trials and errors. Uses specific materials and pictures to help observations.  It counts to 30, and the digits in range 0 to 20, read and count orders.

It helps the students set up a comprehension of the digits and count processes with sequence numbers initially and 20, move from some starting point, count up to 30, and count backward from a particular number between 0 and 20. DeWolf et al. p 72 (2015) state that even you identify the number before and after a given number, the number before and after is defined as one less than (Communicating). You read and use at least one-tenth of the ordinal titles. Recognized the number of items or dots in an entity or dot pattern, dices, and domino point patterns (for instance, Communicating by immediately subitizing small sets of objects (Chang, p 245 2011). They recognize (submit) various arrangements for the same number instantly, for example, different 5. Recognize that it is simple to offer as the way objects are organized (Sadita et al., p 20 2020). Students can also connect number details, numerals, and quantities, including zero.

The number and early learning of operations are essential components of counting. There is a difference between counting by rotation and counting. Students will become familiar with the series if they count back and forth of a certain number. Hence, one-to-one correspondence is calculated; it recognizes that the total number in the set represents the last number name, and a sense of number size, order, and relationships are created. Numbers are essential to developing the meaning of numbers in various ways. Subsidizing requires immediate recognition without counting the number of elements in a tiny array. The word ‘subitize’ comes in Latin and means ‘suddenly’ to come. The expressions “is much like” and “is the same” should be used to reflect group equality. In early stage 1, the word ‘is the same as’ is stressed as it is best suited to the logical comprehension level of the students (Egodawatte, p 103 2009).

Addition and Subtraction

The learners should characterize daily circumstances, behavior, materials, and informal records. Mathematical situations. They explore mathematical problems using artifacts, behavior, technology, and testing and error. Conclusions are supporting the use of concrete materials and paintings. Combines distinguish and compare object sets, explains daily and informal documents. Represent realistic scenarios for sharing and modeling. To model addition, students combine two or more object classes—model subtraction by separating and removing part of an object category. You model and solve fundamental problems with addition and removal with concrete materials or fingertips. Two classes of objects are compared to decide how many more visually displayed numbers are used to support addition and subtraction, for instance, ten frames. Combinations are created and recognized for at least ten numbers.

They explain how students can combine everyday languages, separated and compared, made, joined, connected and, receive, taken from each other, how many more together (Impecoven-Lind & Foegen, p 34 2010). Therefore, clarify or show how a response was received (Communicating, Reasoning). They use techniques that other students have shown (Problem Solving). Examine also different addition and subtraction approaches used in different cultures. Compare forward by way of an added one and backward using sketches, words, and numerals to deduct and record addition and subtraction informally.

Teachers should teach addition and subtraction as a basis for the logical understanding of its inverse correlation in combination with each other. In this sense, the word ‘difference’ refers to the numerical value of the group. It may apply to any attribute in daily language.

Multiplication and Division

It allows a student to explain daily mathematical circumstances, behavior, materials, and informal documentation. They explore mathematical problems using artifacts, behavior, technology, and testing and error. The classes, exchanges, and counts object sets explain them in the daily language and records with informal methods.

The activity helps students study and model fair groups in algebra. Hence also to define an object set. They use the word sharing to explain how objects and models are distributed in equal classes. Recognize groups that are not similar in size and exchange specific materials for solving problems, illustrating, or showing how to receive a reply. Collect and share records by informal methods Label the number of objects grouped and informally shared using images, terms, and numerals in a group record.

Students should manipulate specific materials in all activities (Sewell, 2014). The emphasis is on modeling and defining groups of the same size. Students must learn that fair sharing ensures that all shares are equal. As the students similarly exchange items, the method can be reversed to develop a connection between division and multiplication. Students will first share a group of objects, then assemble all the shared things in a single array. The basis for conceptual interpretation of their opposite relationship should be teaching multiplication and division together.

Students should use the following language to communicate: community, sharing, equality. Sharing – is one thing in several groups, for example, when the student has several pop sticks and three cups and shares the pop sticks one by one in the cups. Cluster – it’s just about dividing the same number of objects into an unknown set of classes like the student is in 12 folding sticks and wants to create groups of 4.

Fractions and Decimals

The student explains everyday vocabulary, behavior, materials, and informal recordings in mathematical circumstances. They use specific materials and pictorial depictions to endorse hypotheses and characterize two parts of them as half-parts (Berlekamp, 2015). They are helping students to define the idea of the half by splitting an object into two equal sections, such as having a piece of belt. Describe to communicate, recognize that halves are two equal parts (Communicating). Malone et al. p 59 (2019) also describe the purpose of dividing an object in a specific manner. They realize that two pieces are not half a whole part and explain why two parts of a whole are half or not. Both pieces are not half as they are not identical” (communication, reasons). In everyday cases, they use the word ‘half’ correctly—record halves of sketches of artifacts.

Some students will define other fractions of daily contexts. It is essential to divide an entire object into two equal parts (Munifah et al., p 224 2019). The emphasis is on fairness in the production of identical parts (Lee et al., p 58 2016). Halves can be of various types. Halves of multiple things can vary in size; for instance, half a sheet of art paper is more significant than a semi a towel. Fractions denote the association between the identical parts and the entire unit.

Students need to speak in whole, part, equal bits, half, halves using the following language. The word “half” is often used daily to denote one of the two parts and not two equal parts; for instance, “have the largest part.” The language of “two equal parts” must be modeled and strengthened when it is half defined.

Patterns and Algebra

It allows students to explain daily language, behavior, documents, and informal records in mathematical situations. It helps students use mathematical problems with artifacts, behavior, technology, and testing and error. To endorse assumptions, use specific materials and pictorial representations. Recognizes, explains, and follows trends (Arcavi et al., 2016). Students sort, categorize and clarify the foundation for these classifications. Sort and divide into smaller classes some everyday things. You recognize the possibility of sorting and classifying a collection of objects in various ways and describe the basis for their classification of objects.

They are copying, continuing, and designing objects and drawings. Using sounds and behaviors, recognize, copy, and repeat patterns. Identifying, copying, continuing, and creating repeatable patterns using forms, objects, or images, for example, using basic computing graphics to begin or continue a repeat pattern. Students recognize when a pattern error happens and describe the wrong thing. The definition often describes a repeated pattern consisting of forms, referring to their distinguishing features (Strother et al., 2016). By this, they repeat the colors.

The development of algebraic thought at later stages needs early-numbering training (including adding and multiplying thinking). Repeating patterns can be formed in the initial stages with sounds, acts, shapes, objects. Using the following language: party, convention, repeat should be allowed to communicate.

They Can Also Perform a “Riddle Me” This Activity

It is a fun lesson for students for Riddle Me.  Depending on the equations you choose, the exercise is simple or complex, but the motivation is to resolve the value of each algebraic equation and find the answer (Zhu & Bayley, p. 34 2013). The student who succeeds in finding the solutions to all the equations wins the activity.

The Hexagon Calculation

This hexagon puzzle is a challenge for algebra that many students will face. The significance of an algebraic expression is calculated via a wave roll (Yildiz, p 120 2013). Students roll the dice in steps, and the number rolls are the ‘n’ value. The student has one chance to use ‘n’ to select a hexagon and to solve the equation. The student with the most solved hexagons scores at the end of the algebraic solution. This course activity offers students an opportunity to work together and have fun in class (Wasserman, p 30 2016).

Conclusion

Evidence-based learning and teaching are a way to understand how teachers can make decisions to enhance learning and teaching, using factual knowledge obtained through research literature and data analysis and data gathered by different methods. Implementing evidence-based learning and teaching can provide organizations with an effective means of improving learning experiences in a holistic approach to enhancing learning and teaching. It is closely linked to other tasks and practices, such as testing and quality assurance. It can benefit from existing data and systems and requires no additional investment. Reflexivity and agency, individual teachers and personnel responsible for the study programs, and the leadership are needed to act upon learning and teaching.

There should also be a set of proposals to understand the evidence-based approach better. An evidence-based approach should be the norm and attributes to training following the critical thinking aspect.

References

Arcavi, A., Drijvers, P., & Stacey, K. (2016). The learning and teaching of algebra: Ideas, insights, and activities. Routledge.

Berlekamp, E. R. (2015). Algebraic coding theory (revised edition). World Scientific.

Caridade, C. M., Encinas, A. H., Martín‐Vaquero, J., & Queiruga‐Dios, A. (2015). CAS and real-life problems to learn basic concepts in the Linear Algebra course. Computer Applications in Engineering Education, 23(4), 567-577.

Chang, J. M. (2011). A practical approach to inquiry-based learning in linear algebra. International Journal of Mathematical Education in Science and Technology, 42(2), 245-259.

DeWolf, M., Bassok, M., & Holyoak, K. J. (2015). From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions. Journal of experimental child psychology, 133, 72-84.

Dörfler, W. (2008). En route from patterns to algebra: Comments and reflections. ZDM, 40(1), 143-160.

Egodawatte, G. (2009). Is Algebra Difficult for All Students?. Acta Didactica Napocensia, 2(4), 101-106.

Impecoven-Lind, L. S., & Foegen, A. (2010). Teaching algebra to students with learning disabilities. Intervention in School and Clinic, 46(1), 31-37.

Knuth, E., Stephens, A., Blanton, M., & Gardiner, A. (2016). Build an early foundation for algebra success. Phi Delta Kappan, 97(6), 65-68.

Lee, H. S., DeWolf, M., Bassok, M., & Holyoak, K. J. (2016). Conceptual and procedural distinctions between fractions and decimals: A cross-national comparison. Cognition, 147, 57-69.

Malone, A. S., Fuchs, L. S., Sterba, S. K., Fuchs, D., & Foreman-Murray, L. (2019). Does an integrated focus on fractions and decimals improve at-risk students’ rational number magnitude performance?. Contemporary Educational Psychology, 59, 101782.

Munifah, M., Romadhona, A. N., Ridhona, I., Ramadhani, R., Umam, R., & Tortop, H. S. (2019). How to Manage Numerical Abilities in Algebra Material?. Al-Jabar: Jurnal Pendidikan Matematika, 10(2), 223-232.

Niaki, S. A., George, C. P., Michailidis, G., & Beal, C. R. (2019, March). Investigating the Usage Patterns of Algebra Nation Tutoring Platform. In Proceedings of the 9th International Conference on Learning Analytics & Knowledge (pp. 481-490).

Sadita, L., Hirashima, T., Hayashi, Y., Wunnasri, W., Pailai, J., Junus, K., & Santoso, H. B. (2020). Collaborative concept mapping with reciprocal kit-build: practical use in a linear algebra course. Research and Practice in Technology Enhanced Learning, 15(1), 1-22.

Sewell, G. (2014). Computational methods of linear algebra. World Scientific Publishing Company.

Strother, S., Brendefur, J. L., Thiede, K., & Appleton, S. (2016). Five key ideas to teach fractions and decimals with understanding. Advances in Social Sciences Research Journal.

Wasserman, N. H. (2016). Abstract algebra for algebra teaching: Influencing school mathematics instruction. Canadian Journal of Science, Mathematics and Technology Education, 16(1), 28-47.

Yildiz Ulus, A. (2013). Teaching the” Diagonalization Concept” in Linear Algebra with Technology: A Case Study at Galatasaray University. Turkish Online Journal of Educational Technology-TOJET, 12(1), 119-130.

Zbiek, R. M., & Larson, M. R. (2015). Teaching strategies to improve algebra learning. The Mathematics Teacher, 108(9), 696-699.

Zhu, H., & Bayley, I. (2013). An algebra of design patterns. ACM Transactions on Software Engineering and Methodology (TOSEM), 22(3), 1-35.