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Annotated Bibliography
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Annotated Bibliography About People, Places and Industries (Annotated Bibliography Sample)


This was a critique of articles in mathematics and ARITHMETIC. It shows the real life application of math with practical ideas for the real world


World of Math
Globally, the education systems considers Mathematics or Arithmetic a crucial foundation course for all learners. This is the study of numbers, quantity, patterns, processes, logic and space among others. Mathematical reasoning comprises of systematic models, which lead to the acquisition of numeracy skills. Therefore, Math is necessary for making scientific deductions and developing numeracy. The difference between Math and Numeracy lies in their concepts. The two also have similarities in application.
The Mathematical calculations facilitate for the development of different discoveriesCITATION Sie12 \l 1033 (Sierinska & Kilpatrick, 2012). Under the mathematic laws, objectivity provides concrete evidence for applications in real life situations. Its classification includes pure and applied mathematics. Pure mathematical concepts such as arithmetic is useful in scientific studies like engineering and physics. It presents ideas and models for studying abstract phenomenon such as abstract research on space distance. Its ideas also provide solutions in applied mathematics for subjects like social research. Mathematics simplifies notions and classifies case studies. Algebra, which is part of its study, provides rules for manipulating numbers. It also comprises of geometry, which focuses on figures, shapes and sizes.
Numeracy is a skill obtained from studying Mathematics. Learners who have the ability to use numbers and Math concepts have numeracy skills CITATION Pur11 \l 1033 (Purpura, Hume, Sims, & Lonigan, 2011). Being literate in Math calls for an ability to reason using numbers. It involves the use of a wide variety of concepts in problem solving. Referred to as logic reasoning or thinking it consists of knowledge in calculations, data interpretation, reading charts, processes and numbers. Reasoning through numbers calls for an understanding of Mathematical concepts such as arithmetic, statistics, geometry, and others. Learners have different levels of numeracy therefore the assessment levels also vary. For example, foundation mathematics teaches basic mathematic concepts like addition, subtraction and multiplication. Advanced learners know how to make deductions from complex concepts like ratios, probabilities and matrices. Professional numeracy involves the use of multiple concepts.
Similarities between Math and Arithmetic
The development of numeracy skills starts at an early stage and develops to maturity depending on the exposure of the learner. Competency in numeracy skills dictates that the learner has the ability to process, make interpretation and communicate mathematic concepts effectively. This calls for a combination of different ideas such as the analysis and interpretation of frequencies, graphs and trends. Thus, Math and numeracy are similar in application. Their concepts overlap during application. Both concepts have evolved over time and they apply to real life situations. Numeracy helps people run bank accounts and make purchases while Math helps business people to make transactions. Both involve the use of numbers for problem solving. The application of Mathematics and numbers is evident in the creation of timetables, and setting the time.
Part 2: Collection of resources
2.1 Theme: Preschool and early numeracy learning
Evidence: Pirjo, A., Pekka, H., Joannes, E. H., & Jari-Matt, V. (2014). The development of early numeracy skills in kindergaten in low-average-and high perfomance groups. Journal of Early Childhood Research, 13(1), 3-16
Description: Pirjo, Pekka, Joannes, & Jari-Matt (2014) note that the development of early numeracy skills in preschool children is different in all children. Though numeracy starts early, there are factors which influence the development of numeracy in preschoolers. Teachers support this development by breaking down complex arithmetic lessons into simple tasks that learners enjoy.
Rationale: This resource supports the mental capacities and the development of numeracy skills. Understanding numbers starts with early development of math skills CITATION Sta17 \l 1033 (Stanberry, 2017). Young learners between 2 and 5 years learn math by counting physical objects from memory. Activities such as measuring water jars, counting bubbles and building blocks simplify math concepts for the learners. Numerical skills acquired through interesting math concepts from real world examples are memorable CITATION Yel11 \l 1033 (Yelland, 2011). However, the mind develops through training and learning activities. Learners need professionally trained teachers to develop complex numerical skills. Although there are inborn abilities, this age group also learns numeracy from exposure CITATION Mor13 \l 1033 (Morales, Calvo, & Bialystok, 2013).
Application: Learning mathematical concepts is easier with practical examples from what children have seen, touched or interacted with and kid’s games are excellent. Computerized games and rhymes also use common themes that children can comprehend. Learning through fun and games or audiovisual shapes children’s memory. Children in preschool learn counting by shapes, numbers and simple charts. In order to acquire numeracy, learners draw, classify and count different items. Singing in numerical themes is one way to motivate arithmetic learning. The preschool themes come to life with experiences that children can connect and interact with when learning. Among these are video clips of activities done with parents and caregivers. Math in the real world reveals challenges and opportunities. Buying items at the groceries provides a number of math ideas for learners. This is a chance for children to learn math addition, subtraction, and shapes. Using a video on the market place reminds children of shopping experiences. Using their favorite fruits helps them to add fruits and vegetables. This age may not be conversant with pricing but will learn counting and subtracting items. Age, vocabulary and attention abilities are some factors, which determine the effectiveness of the learning process CITATION Mel13 \l 1033 (Melissa, Lisa, & Halberda, 2013). Videos, toys, the internet, books, and magazines are some useful learning resources for preschool mathematics.
2.2 Theme: Planned Play and Incidental Play Experiences
Evidence: Robinson, K. (2011). Out of our minds: Learning to be creative. John Wiley & Sons
Description: Using interesting and creative ideas stimulates the learner’s mind CITATION Rob11 \l 1033 (Robinson, 2011). Play based learning curriculum consists of creative games such as dancing, ball games and building blocks. In order to develop numeracy effectively, a teacher adds incidental play experiences in the learning environment. Leaning math is interesting with colorful blocks made of different shapes.
Rationale: Structured play needs planned and incidental experiences because children can recognize shapes and symbols depending on familiarity. Shaping a student’s attitude towards math calls for the incorporation of fun in learning. Further research shows the importance of building blocks in helping students to learn math CITATION Cle11 \l 1033 (Clements, Sarama, Spitler, Lange, & Wolfe, 2011). The resource identifies planned play as effective in the development of math because it relies on research evidence. Planned play includes outdoor and indoor activities that children enjoy. Psychologists and educational researchers encourage the use of creativity in solving problems and brainstorming. However, learning outcome is not always positive and it hinders the child’s ability to become independent in creativity.
Application: Creating a conducive learning environment fosters learning through Incidental play. Children develop math ideas through incidences like drawing. The combination of songs and sequence images helps young learners to connect numbers and their symbols. Having a song board in the play school connects the learner to unplanned learning. This environment is conducive for children with mental challenges like Autism CITATION Bar13 \l 1033 (Baron-Cohen, Tager-Flusberg, & Lombardo, 2013). Shaping arithmetic skills needs both planned and incidental learning activities. This is important because it replaces negative behavior with attention and interactive behavior. Family members and caregivers are important elements in incidental learning because children also grasp information from observation and repeated actionCITATION Jon12 \l 1033 (Jonassen & Land, 2012). Effective and efficient learning involves both formal and informal processes. ECD learning is important in shaping futures math careers therefore a learning institution needs a good plan. Planned play is effective in mentorship programs and professional training. Planned play sticks within the curriculum in order to ensure that learners understand variety of concepts. On the other hand, incidental learning is good for reflective, experimental and impromptu learning. An integrated model provides a comprehensive approach that caters for classroom and out of class learning for the effective development of numeracy CITATION Ent13 \l 1033 (Entwistle, 2013).
2.3 Theme: Mathematics in primary school
Evidence: Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. Educational Studies in mathematics, 79(1), 127-147
Description: Learning mathematics in primary school forms the foundation of careers in mathematics, but does not shape a mathematician. School mathematics has a different focus from its practice in real life. The classroom math has different activities from what mathematician practice. Based on these differences, it is difficult to predict a student’s outcome at primary level.
Rationale: A successful lear...
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