## Foundations of Number Sense

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### Foundations of Number Sense

Chapter 1 of the text (Sousa, 2015) addresses the foundations of number sense and how this ability develops in humans. Unlike other animals with number sense, humans are separated by the ability to count, which is influenced by numerous factors including language. Based on this week’s readings, address each of the following:

• Sousa discusses how children learn to count. How did YOU learn to count? Who taught you? Where and when? Did you use your fingers? Do you still use your fingers?

• Sousa outlines some of the glaring differences between Asian and Western languages when it comes to learning how to count.

o If you teach, or plan to teach, at the elementary level, do you think your students would benefit from learning numbers according to the Asian language patterns? If so, how could you incorporate these patterns without having them learn a new language? If not, what are the drawbacks?

o If you teach, or plan to teach, at the high school or college level, how do you remediate students who struggle with these basic counting and number sense skills?

• Select examples of strategies from pages 26-28 of the text (Sousa, 2015) that you currently use or plan to use. Explain your rationale.

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### Foundations of Number Sense

I learned to count by using a counting chart. I recall that I used to point at numbers on the chart during the counting process. Based on Sousa (2015), the brain imaging played a role in my counting process. The image of the numbers enhanced my counting process. I only used my fingers when adding or subtracting mathematical problems and not counting. Presently, I do not use my fingers in the counting process.

My mind has advanced to be able to count large numbers and carry out addition or subtraction without using my fingers. Moreover, technology has made counting much easier as there are calculators in different devices that can be used in the counting process.

I believe that students will benefit at the elementary level to learn numbers according to the Asian language patterns. My perception is based on Sousa (2015), analysis where the Asian students excel in mathematics when compared to students who learn mathematics using the English language. There are different patterns that I will incorporate into my lessons to enhance their understanding without having them learn a new language.

First, I will concentrate on the repetition of concepts. Secondly, I will break down the syllabus into short units. Lastly, I will introduce games and activities that will have them involved in the lessons. The interest and alertness of the students during the mathematics lesson will improve not only their comprehension of numbers but math as a whole…..

Foundations of Number Sense

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## What Mathematics Means to Me as a Teacher and Learner

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### What Mathematics Means to Me as a Teacher and Learner

What Mathematics Means to Me as a Teacher and Learner-week 1

Details:

1. What do YOU need to know and learn in order to teach mathematics effectively?

2. What do your students need to know and learn for long-term mathematics success?

3. Based on this week’s readings and assignments, have you changed your perspective on mathematics education? If so, how? If not, why?

4. Did you discover something thought provoking in this week’s activities or readings? Explain.

Resources for this week:

Chapter 3. Sousa, D. (2015). How the brain learns mathematics (2nd ed.). Thousand Oaks, CA: Corwin Press.

Links – Common Core State Standards: A New Foundation for Student Success – http://www.hunt-institute.org/resources/2012/09/common-core-state-standards-a-new-foundation-for-student-success/

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### What Mathematics Means to Me as a Teacher and Learner

What do you need to know and learn in order to teach mathematics effectively?

As a teacher the effectiveness of using images to enhance the ability of the students to understand the concepts. According to Sousa, (2015), brain imaging increases the ability of the students to understand the concepts that are being taught. Additionally, one should build on the memory of the students. An instructor should make sure that the students can relate the topic to an earlier lesson that they have been taught. It increases their participation level.

Moreover, the teachers need to have a comprehension of the working memory of their students. This enables them to structure their lesson plans effectively by breaking down them into portions. Small portions make it easy for the students to understand the topic. Lastly, the teachers should be able to discern the suitable learning environment and instructional setting applicable to their students (Sousa, 2015). Students with a disability have different needs and levels of understanding to those without disabilities. The teacher should also be able to detect the emotional stability of their students to enhance their learning experience.

What do your students need to know and learn for long-term mathematics success?

Students need to understand that mathematics is dependent subject. It relates to concepts that they have learned in the lower classes. Moreover, mathematics is an active subject that requires the student to participate in the various activities to enhance their comprehension. Also, mathematics is not about memorization but understanding of the basics. Understanding the basics enables them to be able to solve difficult questions (Sousa, 2015).

Moreover, it increases their ability to manipulate the various aspects of mathematics either in form of simple or word problems. Additionally, Mathematics requires regular practice to reinforce the concepts taught in the minds of the ready. Regular practice will increase their proficiency in manipulating various problems that are presented to them. Finally, mathematics is a fun subject that requires an open mind and readiness from the students to enable them to perform effectively.

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## Learning to Calculate Essay Paper

### Learning to Calculate

Details:

Learning how to multiply can be an extremely difficult aspect of mathematics education. As described in the text (Sousa, 2015), the shift students encounter as they move from counting strategies to the rote learning of arithmetic facts can cause a major upheaval in their thought process.

Keeping this shift in mind, complete the following:

• Based on the information in the text (Sousa, 2015), analyze the multifaceted issue of how American students struggle with multiplication tables and why educators should pay particular attention to student experiences and thought processes while learning them.

• If you teach, or plan to teach, at the elementary level, how do you believe that multiplication tables should be taught? Is it necessary to memorize them? Why or why not?

• If you teach, or plan to teach, at the high school or college level, how do student experiences with multiplication table learning impact students at this level?

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### Learning to Calculate

Based on the information in the text (Sousa,2015). Analyze the multifaceted issue of how American students struggle with multiplication tables and why educators should pay particular attention to student experiences and thought processes while learning them?

The use language in teaching mathematics makes the learning of multiplication difficulties. The addition and subtraction calculations the students are able to associate numbers which makes it easy for them to solve questions. Additionally, there is a consistent pattern that makes the students able to carry backward and forward calculations. Contrariwise multiplications are difficult because the brain is unable to find a sequence that they can relate to. The dissociative aspects of multiplication make learning of the mathematical tables hard (Sousa, 2015). Students have different learning styles that forms a foundation in their arithmetic learning. Paying attention to the learning styles makes them progress to multiplication from addition and subtraction with ease.

If you teach or plan to teach at the elementary level, how do you believe multiplication tables should be taught? If necessary to memorize them? Why or why not?

I believe at the elementary level; the teacher should focus on counting skills of the students. The counting skills are essential in solidifying the learners’ confidence in mathematics. They then can progress to multiplication tables using mathematical charts. In addition, they can start with small figures before progressing to complex ones (Sousa, 2015)…..

Learning to Calculate

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## Demystifying Mathematics

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### Demystifying Mathematics

Order Instructions:

One of the key aspects of mathematics instruction is to instill effective study skills in your students.

Based on the information in chapter 6 of the Sousa (2015) text, answer the following:

* What types of study skills methods do you teach your mathematics students, if any? Do you use Barton & Heidema’s SQRQCQ? RIDD? SQR3? If you do not teach study skills, why do you choose not to do so?

* Discuss, in two paragraphs, the type of mathematics learning strategy you use in your classroom to demystify mathematics OR select a strategy from the text and explain how you will implement it in your classroom and why.

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### Demystifying Mathematics

Discuss the prerequisite skills to learning mathematical concepts. Do you agree with this list? If so what experiences have you had that validated them? If not what skills will you add or remove from this list? Why?

Mathematics educators have proposed 7 prerequisite skills to be used in mathematics leaning process. The first one focuses on following the successive directions that are used in the calculations. This deals with identifying the chronological order in which calculations are conducted to make it easy for the student to duplicate. The second one deals with recognizing the patterns that are used in the mathematics. In learning mathematics, there is always a consistent pattern that distinguishes probability, arithmetic operations, and other topics. Understanding the pattern used in different areas makes calculations easy (Sousa, 2015).

The third one deals with formulating realistic deduction from a question with respect to amount, size, magnitude, and quantity. Additionally, the students need to come up with mental visual pictures. The mental pictures help one to personalize the problem which makes it easy to tackle the problem. The fifth strategy deals with proper space organization and orientation which makes the work clean. In addition, they ensure that one can easily detect a problem in their work as they have organized the workings from one direction to another. The sixth and last strategy deals with deductive and inductive reasoning respectively (Sousa, 2015)…..

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## Writing in Mathematics

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### Writing in Mathematics

Order Instructions:

Based on the information in chapter 8 of the text (Sousa, 2015), write a 2- to 3-paragraph discussion of how you use or will use writing and language in your classroom, whatever your teaching level (currently teaching 8th grade math).

• Why is the use of writing and language important in the mathematics classroom?
• Which learners will benefit from writing about mathematics?
• Which learners will not benefit from writing about mathematics?
• What can you do for those who may not benefit?

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### Writing in Mathematics

Writing in the classroom is an important tool in the learning process. In a mathematics classroom, the practice of writing is important in communicating various mathematical concepts. This is achieved through the higher level of engagement of the brain sparked by writing as the student learns new concepts (Sousa, 2015, pp. 201 – 202). Therefore, the use of writing and language is essential in a mathematics classroom as an enabler of better and deeper learning.

While writing about mathematics is an essential tool in learning various mathematics concepts, not all students will benefit from the practice in the same way. The students who have a practical style of learning tend to benefit most from the use of writing and language in a mathematics class. This includes visual learners, auditory learners, and those who make the best use of tactile and kinesthetic methods of learning (Sousa, 2015, p. 202).

On the other hand, some learners will not benefit much from the use of writing and language in a mathematics class. This category of students includes those who have limited background knowledge and skill level, as well as students who do not have an interest in learning the material or pursuing it further (2015, pp. 205 – 206)….

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## Statistics: Scatterplots Essay Paper

Statistics: Scatterplots

Question 1

Scatterplots have been ranked as one of the oldest and most common techniques for projecting high dimensional data to 2-dimensional form. Generally, these projections are arranged in a grid structure to aid the user in remembering the dimensions linked with each projection. Scatterplots have proven to be quite useful in determining the relationship between two variables.

Scatterplots have been linked with a number of benefits. For instance, the plots have been cited as one of the most important technique for studying non-linear pattern. Krzywinski & Altman (2014) state that it is easy to plot the diagram.  It is also useful in indicating the range of data flow, that is, the minimum and maximum value. Observation and reading of data in scatterplots is also straightforward.

Scatterplots are also important in studying large data quantities and make it easier to see the relationship between variables and their clustering effects. The use of scatterplots is an invaluable which is also useful in analyzing continuous data. However, this technique has a number of shortcomings such as being restricted generally to orthogonal views as well as challenges in projecting the relationship that exists in more two dimensions.

Question 2

When determining the appropriateness of the inferential statistical techniques, the researcher should first know if his/her data is arranged in a nested or crossed manner. If data is in a crossed manner, all study groups should have all intervention aspects. However, in a nested arrangement each study group will be subjected to a different variable. The correlation of variables can also be used in determining the appropriateness of a technique.

If the two variables have a linear or closely related association, the technique is said to be suitable. The number of assumptions that are employed when using a technique are also useful indicators. For instance, some techniques such as the t-test have several assumptions compared to the ANOVA technique, this implies that t-test has a large room for study errors unlike the ANOVA test.

Question 3

The Pearson product-moment correlation coefficient (PPMCC) is an analytical technique that is applied in indicating the strength of a linear association between two variables. This technique indicates a line of best fit through the data of two variables. It takes values ranging from +1 to -1 whereby a value of zero indicates that two variables of study do not have any association.

Values that are less than zero indicate that the two study variables have a negative association such that when one value increases the other one decreases. On the other hand, values that are greater than zero indicate that they have a positive association between them, that is, when there is an increase in one value, the other value increases as well. To determine whether the two variables have a linear relationship, they are fist plotted on a graph followed by a visual inspection of the shape of the graph.

A section of some scholars used to argue that PMCC can be used to indicate the gradient of a line. However, recent studies have dismissed this claim. For instance, Puth, Neuhäuser & Ruxton (2014) illustrate clearly that a coefficient of +1 does not mean that when one variable increases by one unit the other one increases by the same margin. A coefficient of +1 means that no variation exists between the plots and the line of best fit.

A number of assumptions must be put into consideration by analysts when they use the PPMCC. For instance, it is assumed that the outliers are either maintain at a minimum or removed completely. However, this is not the case in majority of studies. Another assumption is that the variables used should be distributed approximately normally and they must either be ratio or interval measurements.

References

Krzywinski, M., & Altman, N. (2014). Points of significance: visualizing samples with box plots. Nature methods, 11(2), 119-120.

Puth, M. T., Neuhäuser, M., & Ruxton, G. D. (2014). Effective use of Pearson’s product–moment correlation coefficient. Animal Behaviour, 93, 183-189.