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## Definition of Progression in learning

A series of numbers in which the following number is produced by adding an integer equal to the first one for each pair of successive terms is known as a mathematical sequence or progression. We will encounter several keywords in AP, indicated by the following: first term (a) Similar distinction (d) Term (an) nth addition of the initial n terms (Sn) (Muhtarom et al.,2019). The characteristic of calculation progression is represented by all three components. The subsequent part will provide further information on these three attributes.

## Nature of Mathematics As a Subject

Mathematics is an alphabetical system. It denotes fundamental mathematical phrases, symbols, and formulas. The goal of the math curriculum is to assist all kids in Having a positive outlook on maths and seeing its usefulness in everyday life. Gain proficiency in figuring out solutions and applying maths to daily situations. Employ precise and effective terms for mathematics. Recognize numerical ideas and procedures at a level appropriate for their maturity and aptitude Gain mastery of basic arithmetic concepts and the ability to remember basic numerical facts.Math skills in kindergarten, including comprehending number sequence, tallying up, ordinality, proportion, addition, and subtraction, were examined in a meta-analytic model(Csíkoset al.,2020).

## Importance of Progression in Learning

Mathematics needs to be purposefully promoted in kindergarten. Encouragement of overarching mathematical skills that align with young minds and are fundamental to numeracy. Regarding card and game tables, according to instructors, they are useful for helping students acquire mathematical skills. This strategy is controlling the play environment's structure and accessibility to the kids. Amidst them, the quantity–number–competencies are particularly significant as long-term studies found: that quantity–number–competencies at preschool admission are the biggest predictor for proficiency in mathematics in the subsequent grade of class. Engaged with the quantity-number-abilities at school admission are the best indicators of mathematics success in the third grade, indicating the importance of these competencies. Kindergarten must improve possibilities for every kid, irrespective of their family circumstances (Muhtarom et al.,2019). Joyful elements were discovered to be the most reliable indicators of future academic success.

## Learning Progression As a Pedagogy For Teaching Mathematics to Early Learners

This pedagogical sequence of modeling, increasing reduction of scaffolding, and extension may be used to enhance the education of kids in a variety of play scenarios. Pedagogical progression and transition(Ward et al.,2020). To provide students the opportunity to practice evaluating both peers' work, expose them to group procedures, and lead them through a few warm-up activities. Think about assigning duties to pupils or dividing up the job among them. As a substitute, the project may ask students to adopt other stances, especially those of local company owners, elected figures, etc.

### Justification of Rogression Theory

As previously mentioned, the progression method is also inherent in nascent literacy and numeracy activities, where teachers actively teach kids the importance of representing and quantifying objects using symbols. Four components are necessary for play-based methods in Elementary school instruction and mathematics. (i) The "substance in mathematics must be a component of the game's mechanics; (ii) must be "properly portrayed"; (iii) "essential for more education moreover, the game must be "suitable for somebody's learning" (iv) requirements of the kid(Tomlinsonet al.,2019).

The time and Money concept defies Math as a ubiquitous and significant part of our lives, utilized in everything from marketing to cooking to handling our cash flow to playing sports. Several occupations, including science, engineering, health care, and banking, also utilize it. Early arithmetic instruction will provide kids with a solid basis for success in school and the workplace.

## Critics of Researchers on Learning Pedagogy

• ### Progression theory used in teaching maths

A collection of teaching strategies, such as instructional activities, learning settings, and three-way interactions, that are connected to all of the thinking stages in the developmental progression make up the third section of an academic trajectory. The purpose of these activities is to teach kids the concepts and abilities required to develop their analytical skills to the next level.The numerical abilities of a kindergarten-aged child can be used to forecast their future literacy and math competence. Some important math concepts for kindergarten children are:
Probability, Since every kid is unique, with varying interests, abilities, and needs, mathematics was designed for students in elementary through eighth grade. Both math and language are essential. Kindergarten math lessons often begin with teaching children the names of numerals and how to write amounts from 1 to 10.

Preceding Numbers, As they advance, they comprehend the idea of numbering and realize that, while calculating the number of things, the quantity present represents the last value counted, which represents objects.

Shapes and Graphs, Together with counting, kindergarteners also practice comparing one number to another, ordinal number recognition (first, second, and third), and the mere beginnings of skip counting by groups of numbers, such as twos, fives, and tens, utilizing resources such as a numerical line or several hundred board.

Adding and Subtracting, Instructors can assist young students with categorizing and arranging common items based on shared characteristics such as color, size, and form. Toys or other commonplace items can be used for sorting exercises.

Sorting and Classifying, Children learn about fundamental shapes including shapes such as rectangles, triangles, squared amounts, and circles in kindergarten.They use their fingertips and hands to measure length and area, blocks or squares to measure area, and water or sand to measure capacity.

In contrast, Along with learning to read graphs, they additionally acquire data interpretation. Children will need this crucial ability throughout their scholastic lives in sciences and mathematics studies. Early measurement techniques are used in many of the daily tasks that kids do.

Measuring and Comparing, Children will learn the fundamentals of financial literacy in preschool. Additionally, they might start counting pennies. In later grades, understanding resources helps kids grasp other mathematical principles like fractions and exponents.

• ### How do teachers make math fun for kindergarten students?

Educators may engage kindergarten kids in arithmetic by using games, riddles, and practical exercises. They can also connect arithmetic to everyday life by using examples from real-world situations.Instructors include the kid actively participating, lacking external goals, and frequently incorporating pretend play(Trenholm et al.,2019). Assessing the children in attendance, comparing amounts when distributing equitably, and executing one-to-one correspondence while setting the table are all part of the conceptual framework for the formation of quantity-number competencies. Teachers must choose the most effective strategies to assist kindergarteners in gaining these abilities.

## 3 Ways to Help Children with Kindergarten Math

### ⦁ Problem-Solving

Decide on your evaluation and assessment criteria for the task. Think about including peer and personal evaluations in the project's grade(Voigt et al., 2020).
some curriculums are

• A curriculum as opposed to a free learning environment,
•  Fostering children specifically at risk as opposed to nurturing all children, and
• concentrating solely on domain-driven abilities as opposed to taking a more comprehensive approach.
• creative approaches to preschool mathematics should also be in line with elementary pedagogy. Kindergarteners have a strong desire to learn and are highly motivated to participate actively in their education.

### ⦁ Classroom Management

Kindergarten teachers may engage kindergarten kids in arithmetic by using games, riddles, and practical exercises. They can also connect arithmetic to everyday life by using examples from real-world situations.

Subject-focused news ,they were questioned to explain how they carried out the intervention and how the kids interacted with the measure and—as a comprehensive assessment to end things.

Methods of conversation, the students were split into three categories based on the prior test math proficiency to see if they would benefit from the instruction differently depending on their level of competency.

Respect and relationship with students Teachers' evaluation of appropriateness and learning outcomes. By attentively listening to the student's responses and considering them, the instructor can gain further insight into the learner and the assignment topic by asking some additional questions (Bosioet al.,2021).Nearly all of the teachers in both groups spoke highly of the supplied content.

## Different Theories in Learning Progression

Vygotsky's theory, according to which usages of the sign are an essential component of concept development, can establish a connection between the production of ideas and several numerical activities, including ones that are disliked by many educators. According to Piaget's theory, a teacher should analyze a student's work to get a deeper understanding of his thinking while also encouraging the student to self-check, estimate reflect, and explain. When teaching youngsters numbers, it's important to utilize amounts and numbers that have significance for them. Mathematics Richard Skemp went on to study psychology1. He used concepts from each of these fields to illustrate how arithmetic is learned(Verschaffelet al.,2020). His primary 'push' in his argument is that students create schemata to connect new information to what they currently know. Best theory in progression used in teaching maths in early learners

Among many others, Zoltan Dienes hypothesized that children might learn more complex math at an earlier age than previously believed by utilizing interactive materials, games, and tales. Additionally, he created logic blocks and mathematical materials, which planted the roots for the modern usage of manipulative in education (Rezaet al.,2021). As a result, kindergarten is the ideal age to expose kids to the foundational ideas of mathematics, which will hopefully spark a lifelong interest in the subject. We will examine the arithmetic ideas that kindergarteners usually learn in this guide, giving parents and teachers a thorough grasp of what math is taught to kids in kindergarten.

• ### Authors against progression in learning

Paul Erdos’snumber theory and combinatorics questioned in what ways children’s beliefs change from the start of the course to the completion of the field expertise. Terence Tao a mathematician of partial differential equations asked how the objectives and summaries of the collaborating instructors, field administrator, and program instructor match those of the interns' accounts and assessments of what they experienced in the classroom and on the job? John Horton Conway’s The Surreal Numbers what are the opinions held by three preserves primary teachers regarding the following? Justifications for altering the strategy, the teachers assisted the kids and presented the activities(Rezaet al.,2021).

• ### Interaction & Association

Kindergarten math using card and board games is compared to a curriculum program addressing children's academic achievement and learners as the following primary research issue is discussed. Subject-specific correctness, like Flip the Box and Putting up the Fives, need adjustments to the rules or materials; and still others, like More is More, were created just for the project they had to play the "computation games" that were in the box(Delgado-Rebolledo et al.,2020).

In response to statements made by students, the exam consists of questions on ordinarily, cardinality, amount, number knowledge, and basic mathematical procedures. It frequently moves from problems with picture illustrations integrated into real-world narratives to ones with solely numerical representations(Lauet al.,2021).

• ### Math Is All Around Us

Children with greater abilities are not catered for in the training course. Separated outcomes were investigated by splitting the kids into three categories: a high-level group was formed by a third of the sample as determined by their pretest math proficiency.

Addressing disruptions,the study can conclude that group training sessions have a potential risk of negative outcomes. The differential numerical findings match the instructors' evaluation of learning improvements based on their daily observations. Additionally, they explained that while the play-based approach benefited all children, the classroom program was most helpful for those with extremely poor proficiency(Csíkos et al.,2021).
Personal accessibility and dependability,the ability to repeat mathematical procedures, and the incentive of a peer-group environment, where participants watch out for and encourage one another, are the unique potentials of deck and board games. It is evident from the responses provided that instructors were more in favor of a play-based approach. The youngsters in this research may have had better learning outcomes because of their optimistic outlook.

• ### The ALACT Model on Progression Theory

First,the progression model utilizes the ALACT methodology to connect theory and practice necessitating regularly switching up school days and holding special sessions designed to enhance educational experiences. Secondly, tight collaboration between the teacher learning center and the schools is required to harmonize the actions of mentor teachers located in schools and instructional specialists based in the institute (Csanadi et al.,2021). The foundation of realistic and applicable teacher learning is structures developed through experiences; teaching encounters are not as disjointed as the layout of many teaching-education programs would have us believe (Kayaet al.,2021). A teacher's capacity progression model for deep empathy and understanding of the inner workings of their students. It is crucial that the instructor continuously enforces the rules against disruptions, which also means that he must follow them himself. If the instructor is well-prepared and exudes confidence in subject-specific situations, this sensation will be attained (Nováková,2019).Instructors in particular should avoid becoming too close to their students. During working phases when the students are not paying close attention to him, the instructor should nonetheless be there at all times. Method-oriented classes emphasize scientific information, whereas subject-relevant lessons concentrate on imparting broad techniques and avenues of knowledge. Different strategies can be used to structure classroom discussions. The methods the instructor uses will determine whether or not they are effective(Balbay, 2019). When a teacher guides a course in the correct path, a lesson that follows his plan precisely reflects restrained leadership. Students have significantly more opportunities to shape the format of a lesson in a class with loose management. It may become necessary for a teacher to depart from his lecture plan; in such case, he must explain the decision to the teammate who is watching. An unexpected strategy, like visiting a scientific center, should be employed to pique the student's interest in a new subject. It also implies that if a scheduled activity does not go as expected during the class.

## Benefits of ALACT

Progression-based approach with this concept, there are five distinct stages or steps: (1) action, (2) reflection on the action, (3) recognition of the key elements, (4) development of other action strategies, and (5) trial, which is an experiment in and of itself and, therefore, the beginning of a new cycle. It is sometimes challenging for the professors to include the answers to every one of those queries. The inquiries in the progression theory in particular are frequently challenging since teachers don't always know what their pupils are thinking or feeling.

## Assumptions and Future Plan

The ALACT model outlines a methodical progression approach to reflection, but it gives little information regarding the subject matter of that reflection—that is, what the instructor should reflect on. It is a helpful model for expanding the previously mentioned processes. It has six stages that can affect how well a teacher performs (Jinet al.,2019). The five categories of the progression approach are identity, which refers to an individual's understanding of themselves; progression behaviour, which refers to an individual's behaviour (both productive and ineffective); abilities, which include an individual's various skills; identity, which refers to an individual's understanding of themselves; and mission, which refers to an individual's tasks and sources of inspiration. What matters is that it should assist the instructor in accepting the aspects of the circumstance that are significant for determining the appropriate course of action.

## References

Balbay, S., 2019. Enhancing critical awareness through Socratic pedagogy. Eurasian Journal of Applied Linguistics, 5(3), pp.515-536. Accessed on 16.11.23https://dergipark.org.tr/en/pub/ejal/article/651348
Bosio, E. and Schattle, H., 2021. Ethical global citizenship education: From neoliberalism to a values-based pedagogy. Prospects, pp.1-11.Accessed on 16.11.23 https://link.springer.com/article/10.1007/s11125-021-09571-9
Csanadi, A., Kollar, I. and Fischer, F., 2021. Pre-service teachers’ evidence-based reasoning during pedagogical problem-solving: better together? European Journal of Psychology of Education, 36, pp.147-168.Accessed on 16.11.23 https://link.springer.com/article/10.1007/s10212-020-00467-4
Csíkos, C. and Szitányi, J., 2020. Teachers’ pedagogical content knowledge in teaching word problem-solving strategies. ZDM, 52(1), pp.165-178.Accessed on 16.11.23 https://link.springer.com/article/10.1007/s11858-019-01115-y
Delgado-Rebolledo, R. and Zakaryan, D., 2020. Relationships between the knowledge of practices in mathematics and the pedagogical content knowledge of a mathematics lecturer. International Journal of Science and Mathematics Education, 18, pp.567-587.Accessed on 16.11.23 https://link.springer.com/article/10.1007/s10763-019-09977-0
Duschl, R.A., 2019. Learning progressions: Framing and designing coherent sequences for STEM education. Disciplinary and Interdisciplinary Science Education Research, 1(1), pp.1-10.Accessed on 16.11.23 https://diser.springeropen.com/articles/10.1186/s43031-019-0005-x
Jin, H., Mikeska, J.N., Hokayem, H. and Mavronikolas, E., 2019. Toward coherence in curriculum, instruction, and assessment: A review of learning progression literature. Science Education, 103(5), pp.1206-1234.Accessed on 16.11.23 https://onlinelibrary.wiley.com/doi/pdf/10.1002/sce.21525
Kokka, K., 2020. Social justice pedagogy for whom? Developing privileged students’ critical mathematics consciousness. The Urban Review, 52(4), pp.778-803.Accessed on 16.11.23 https://www.academia.edu/download/63732462/Kokka_2020_Social_Justice_Pedagogy_For_Whom20200624-9607-vjsp02.pdf
Kaya, G. and Öz, S., 2021. Investigation of the Effect of Teacher Training Programs on Reflective Thinking: ALACT Model. International Journal of Progressive Education, 17(2), pp.275-291.Accessed on 16.11.23 https://eric.ed.gov/?id=EJ1293295
König, J., Blömeke, S., Jentsch, A., Schlesinger, L., née Nehls, C.F., Musekamp, F. and Kaiser, G., 2021. The links between pedagogical competence, instructional quality, and mathematics achievement in the lower secondary classroom. Educational Studies in Mathematics, 107, pp.189-212.Accessed on 16.11.23 https://link.springer.com/article/10.1007/s10649-020-10021-0
Lau, E., Chai, K.K., Goteng, G.L. and Wijeratne, V., 2021. A Neural Network Modelling and Prediction of Students' Progression in Learning: A Hybrid Pedagogic Method. In CSEDU (1) (pp. 84-91).Accessed on 16.11.23 https://www.scitepress.org/Papers/2021/104056/104056.pdf
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Nováková, E., 2019, August. Reflection of video recordings as a part of the creation process of prospective kindergarten teachers’ professional portfolios. In J. Novotná & H. Moraová (Eds.). International Symposium Elementary Mathematics Teaching: Opportunities in Learning and Teaching Elementary Mathematics (pp. 271-279).Accessed on 16.11.23 https://www.academia.edu/download/61104923/proceedings-19.pdf#page=271
Rezat, S., Fan, L. and Pepin, B., 2021. Mathematics textbooks and curriculum resources as instruments for change. ZDM–Mathematics Education, 53, pp.1189-1206.Accessed on 16.11.23 https://link.springer.com/article/10.1007/s11858-021-01309-3
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Voigt, M., Fredriksen, H. and Rasmussen, C., 2020. Leveraging the design heuristics of realistic mathematics education and culturally responsive pedagogy to create a richer flipped classroom calculus curriculum. ZDM, 52, pp.1051-1062.Accessed on 16.11.23 https://drive.google.com/file/d/1wfKszwYSk13I4_4W7X9LVgHLf78fh733/view
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