Good Article Review On Learning Task Portfolio Activity 2
The purpose of this paper is to reflect on my individual learning journey, by investigating three activities which were undertaken in tutorials. These activities provide learners with a unique experience which encourages learners to become acquainted with mathematical logic.
ACTIVITY ONE: NUMERACY EVERYDAY – MATH ANXIETY
PURPOSE OF ACTIVITY
The purpose of this activity, ‘Numeracy Everyday’, is to provide a further understanding on the significance of numeracy in our everyday life. This activity incorporates the idea of mathematical identity, as it provides an individual, like me, who considers themselves with a high level of math anxiety, to come to the realisation the regular use of mathematical concepts in our daily life.
BACKGROUND/ CONTEXUAL INFORMATION
The nature of numeracy is practiced daily, sometimes it goes unaware that the nature of mathematics is so apparent in for example, adding shipping & handling when online shopping, driving different distances, .buying gas for the car, and calculating savings using coupons are only a few ways math is used every day. People do not notice they are calculating math because the activities are daily activities that go by without being noticed.
Traditional views on acquiring mathematic knowledge used the main strategy of rote learning, repetition and memorisation. This approach left learners with a solution, although without any understanding of concept behind the solution.
Today, the more practical strategy is to use Everyday Mathematics and the concrete concepts of place value to operational algorithms to provide learners with a conceptual understanding of addition, subtraction and other types of calculation by building on the skills the children have as well as observation and communication skills.
Cooperative learning allows children to work in groups to find solutions. A student may notice that they use numbers every when they program the microwave to heat up a sandwich or slice of pizza. Another student in the group might observe that her grandmother does not know how to use a calculator. The children discuss within their group how they use numbers. Together they think about the devices they have that their grandparents never used when they were young.
RELEVANCE TO OWN LEARNING
Throughout this learning experience, .I was surprised by the comments the students made to each other, it allowed me to clarify my general perspective on mathematical concepts and the recurrent use in my daily life. Personally, I grew up maintaining negative connotations toward math, I think, due to having old fashioned teachers in Primary School, who never explained the basics as they practiced rote learning strategies, which left me without the fundamentals of understanding mathematics. This has largely implicated my ability to succeed in mathematics, even throughout high school I was fearful, if I failed even If I tried, because I lacked basic foundations and I didn’t want to feel embarrassed.
It allowed me, to further concrete my mathematical language by writing and then, discussing, and therefore refreshing and strengthening my technical mathematic vocabulary.
This activity also highlighted that many mathematical terms, like foot, also have different meanings in the English language. For example, foot can mean foot on the end of your leg and a foot that measures 12 inches. Another example is the work difference, the difference between two numbers means to subtract, but the difference between two pictures is a comparison about the two pictures.
Koehler (2002: 191) wrote about how teachers organize information and then use narrative form to verbally explain how to apply it. I now understand better how the different steps used in teaching complement each other and help the learning process. While teaching, I organized and applied information while explaining verbally different aspects of the information. Using the narrative together with the other steps helped increase my knowledge.
LINKS TO REAL LIFE SUPPORT WITH ARTICLE
The connection between math anxiety and actual math performance in learners is apparent (Ramirez, Gunderson, Levine, and Beilock 2013). Ramirez (et al. 2013) showed that math anxiety occurs in first- and second-graders and results in poor grades. The researchers recommended that math anxiety in young children be identified and treated so good students will not give up on math at a young age (Ramirez et al. 2013).
The understanding that terms used may have multiple meanings the more familiar learners become with the terms, the more able they are to apply it in a classroom situation (Rubenstein and Thompson 2002). Rubenstein and Thompson (2002) share the example that students can see the equator is equal distance from the North Pole and the South Pole.
Supports learner development as it provides a visual understanding and encourages learners to discuss their positional movements using mathematical terms which allow them to interpret real life situations.
ACTIVITY TWO: LARGEST AND SMALLEST – PLACE VALUE
PURPOSE OF ACTIVITY AND
The purpose of this activity, ‘Largest and Smallest’, is to familiarise learners with the concept of place value and the mathematical language associated with the term. It does this by providing a physical/visual representation a teaching strategy, allowing learners to visually comprehend the positional value of each digit. The positional value of each value remains a central aspect in understanding in the Hindu Arabic numeration system. This practical teaching tool allows for learners to further engage with the activity of moving the digit in a number in order to make a larger or smaller value.
BACKGROUND/ CONTEXUAL INFORMATION
The concept of place value is a fundamental basis of understanding the Hindu-Arabic numeration system. This refers to the base ten system and ten units like blocks equal one long unit.
Base ten refers to the system we use, having ten numerals although depending on the place value of the numeral, multi digit expressions are taught. The numeral is the symbol that represents a number. For example, ten units with ten blocks each equal 100 or 10 units of 10.0 = 100.0; the digit moves to the right because the number increases in value.
This could mean that without recognising place, a learner may find it difficult to understand numbers and making calculations. Understanding place is important so that larger and smaller numbers are understood depending on the place value.
The ten numerals (or digits) are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
HISTORICAL SIGNIFICANCETen fingers and ten toes are two sets of base 10, because the numeral – zero (0) is included with the number 1-9. Zero is a place-holder because to really understand the value 5 without a zero is impossible. Is it 5, 50 0r 500? Base 10 makes addition and multiplication possible without having to use many, many numerals. 28 plus has 20 in the tens place and 8 in the ones place so adding 1 more in the one’s place equals 29; 20 + 8 +1 + 29
RELEVANCE TO OWN LEARNING LITERATURE REFERENCE
This activity provided me with the basic knowledge of numeracy which is a crucial aspect in understanding simple algorithms. I understand that algorithms can be very simple and used over and over again (Ironwood 2006). Algorithms are not only important to computer scientists, they are important to everyone. Algorithms are steps that are used to solve a problem.
Learning base 10 is an essential basic tool that allows us to calculate values by adding, subtracting, multiplying and dividing in elementary school. Students learning base learn to understand place value and that is key to be able to count. Using computation to solve number problems uses algorithms (Ironwood 2006).
LINKS TO THE REAL LIFE CONTEXT SUPPORT WITH ARTICLE
The Hindu- Arabic numeration system is the most frequently used system, as we apply it to our daily lives. The use of base 10 makes computations easier. The types of computations are used so often we often take them for granted, like adding up the cost of a bag of groceries, balancing a checkbook, or making a simple budget using a week’s allowance (Ironwood 2006).
Without understanding the importance of place value and the value each digit holds a child or an adult cannot carry out simple operations like adding, subtracting, multiplication and division in order to solve a problem.
Enhancing the use of numbers, zero was used as a placeholder when it was first invented in India, but now it is considered a number.
As society developed, so did the symbols used to represent numerals (digits). Numerals are 0 to 9. We use base 10 so when we add one to 9 we add another place to zero: 10 (O’Connor and Robertson 2000).
Logical and formal mathematics are not appropriate to teach to young people now, because they need to understand algorithms and other concepts that are part of the high technology and computer age. Everyday Math is presenting math logically and the same mathematical information is learned as with formal or traditional teaching methods. Everyday math makes learning math more relevant to children and helps their communication skills.
A teacher using Everyday Math indicates the meaning offractions logically, by explain that division is the “inverse of multiplication” and “building on their previous knowledge” teaches fractions (Askey 1999).
ACTIVITIY THREE- CLOCK FACE ANGELS
PURPOSE OF ACTIVITY
The aim of this activity is to broaden the learner’s mathematical understanding by showing them how a clock with two hands makes angles. The angles are repeated at certain times, when the same amount of degrees is between the hour and minute hands.
The teaching strategy used in this activity is problem solving, which allows learners to use their mathematical logic to .visually and critically develop problem solving skills .The students can look at the clocks with hands and work together to think about angles. The clock face angle activity uses and everyday device, the clock to help children enhance their thought process so they can arrive to a solution. Developing computer age a meaning for angle with the clock helps students understand what an angle means: where two hands, lines, or arrows that shares only one end, but the other end is different for each hand.
BACKGROUND/ CONTEXUAL INFORMATION
The nature of numeracy is practiced daily; sometimes it goes unaware that the nature of mathematics is embedded in so many daily activities.
Individuals are .not usually aware of how to break down the problem into more manageable solvable steps to finally reach the desired answer, even though they do so every time they make a simple computation in their daily lives. Understanding that numbers are used often during the day, and then breaking down the steps, builds a good foundation for learning math.
The activity teaches about other ways that time can be measured. For example, in ancient times, a sundial was used. Another activity is to turn off the classroom lights, and show how a stationery pen light shines light upon the globe. The understanding is important to understand the passing of time and the concept of time zones.
RELEVANCE TO OWN LEARNING
The clock activity expanded my understanding because I learned how to think about time zones using my intuition instead of looking up the time in different parts of the world on the computer. I also thought about how angles (like the angles of sun rays on the globe) have meaning in our lives, not only in geometry (Aresta, Crowley, Ruoppo, and Schwass 2005).
Relate it to other real life situations: children who take music and singing may already understand the importance of time using music as the basic concept. An analog clock has hands, but digital clocks show the time by numbers (Aresta et al. 2005) I learned how to teach that both types of clock were showing the same measurement for time, but in different ways.
It allows the learner to interpret the issue, by analysing the question about how time is measured. A question may be how a sundial can tell the same time as a clock, and that will help the student understand a new concept of measurements using the angles of the clock or angles to sun rays. This complex problem involves learners to evaluate many ideas that are part of the modern world. For example how people in other parts of the world eat their breakfast at a different time than the students. Also that the same measurement can be taken in different ways; so there is not only one measurement to measure time.
LINKS TO REAL LIFE
Realistic application to real life math concepts helps students learn using active games or lessons. Active learning is better than passive learning in some ways; but the important thing to remember is active and passive learning are both very important (Jacobsen, Eggen, and Kaucahk 2009). Telling time is used so many times a day that people rarely, i fever think of it as ‘doing math.’ Learning about angles is a basic concept that the students will build upon during their school years.
Aresta, M., Crowley, B., Ruoppo, N., and Schwass, D. (2005) “Exploring Mathematics using the Clock and Timekeeping,” Eastern Connecticut State University, http://www.easternct.edu/~koiralah/TimeUnit.htm
Askey, R. (1999) ‘Know and Teach Elementary Mathematics,’ American Educator/American Teachers Federation, http://www.aft.org/sites/default/files/periodicals/amed1.pdf
Eggen, P. & Kauchak, D. (2004). Educational psychology: Windows on classrooms. Columbus, OH: Pearson, Merrill-Prentice Hall.
Jacobson, D.A., Eggen, P, and Kauchak, D. (2009). Methods for Teaching: Promoting Student Learning in K-12 Classrooms. 8th ed. Boston: Allyn & Bacon.
Koehler, M. J. (2002). Designing case-based hypermedia for developing understanding of children’s mathematical reasoning. Cognition and Instruction, 20, 151–195, http://mkoehler.educ.msu.edu/OtherPages/Koehler_Pubs/Koehler_CI_2002.pdf
Gerardo Ramirez, G., Gunderson, E.A, Levine, S.C., and Beilock, S. L. (2013): Math Anxiety, Working Memory, and Math Achievement in Early Elementary School, Journal of Cognition and Development, 14:2, 187-202 http://dx.doi.org/10.1080/15248372.2012.664593
Rubenstein, R. N. and Thompson, D.R. (2002). “Understanding and Supporting Children’s Mathematical Vocabulary Development” Teaching Children Mathematics, October, pp. 107 -112, http://www.fredonia.edu/faculty/education/pickreign/edu640/TCM2002-10-107a.pdf
Ironwood and Twin Peaks Elementary School. (2006). A guide to Everyday Mathematics Arithmetic Algorithms in MUSD, http://www.maranausd.org/DocumentCenter/Home/View/929
O’Connor, J.J. and Robertson, E.F. (2000). “A history of Z,” MacTutor History of Mathematics http://www-history.mcs.st-andrews.ac.uk/HistTopics/Zero.html
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