## 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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## Introduction of the Common Core State Standards

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### Introduction of the Common Core State Standards

Details:

The most recent attempt to increase student learning and achievement in our educational system was the introduction of the Common Core State Standards. This collaborative effort was designed to bring together a set of comprehensive standards that focused on getting students “college and career ready.”

Based on information in the video Common Core State Standards: A New Foundation for Student Success (Hunt Institute, 2011), the website About the Standards (Common Core State Standards Initiative, 2015), and any other credible sources you choose, answer the following questions:

• Who collaborated to write the standards?o What is your reaction to the representatives involved?
• What did the writers of the standards aim to achieve in regards to mathematics instruction and learning?
• What major differences do you notice between the CCSSM and previous standards used by your school or district?

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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### Introduction of the Common Core State Standards

#### Who collaborated to write the standards?

The introduction of the Common Core State Standards resulted from the collaboration between the National Governors Association and various state education chiefs of at least 42 states (The Hunt Institute, 2012).

#### What is your reaction to the representatives involved?

The representatives involved in the writing of the standards present a holistic representation of interested parties in the education system. The project involves the Council of Chief State School Officers, the National Governors Association Center for Best Practices and a variety of other experts in various fields of business and knowledge (The Hunt Institute, 2012). This provides a sufficient mix and representation to ensure the quality development of standards as well as efficient delivery of the same (Common Core Standards Initiative, 2016).

#### What did the writers of the standards aim to achieve in regards to mathematics instruction and learning?

With regard to the teaching and learning of Mathematics, the standards aim to achieve greater coherence of the teaching and learning of the curriculum. In this case, the learners and instructors ought to make sense of the problems, gain the ability to think in the abstract, understand arguments and provide meaningful critique, gain the proficiency to model with math, express regularity in repeated reasoning, and use appropriate tools strategically (Common Core State Standards Initiatives , 2011)…..

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## Enhancing Subitizing Essay Paper

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### Enhancing Subitizing

Order Instructions:

This week, you have focused on how the preschool and kindergarten brain learns mathematics. Using information from the TouchMath: How It Works (Innovative Learning Concepts, n.d.) website and chapter 5 in the text (Sousa, 2015), do the following:

Explain in 3 pages how TouchMath and the game of Dominoes can facilitate a deep understanding of basic mathematical operations.Include multisensory applications, such as using “audio input” while identifying number patterns, which can be found in the sample counting game at DreamBox (DreamBox Learning, n.d.). Include your own strategies, too!

Enhancing Subitizing

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### Enhancing Subitizing

Enhancing learning of mathematics is a key research concern for many scholars and education providers. A common principle identified from numerous research on learning patterns is the need to engage quality learning from an early age. Among the most successful methods of learning mathematics at the pre-adolescent stage is the use of subitizing. Subitizing is the ability to enumerate a small set of data in a rapid and accurate manner (Revkin, Piazza, Izard, Cohen, & Dehaene, 2008).

Despite the numerous debate on various issues around the topic, the use of subitizing is key towards learning, especially for pre-adolescent learners. This paper looks into the usefulness of a number of methods linked to subitizing as well as how these methods aid in the gaining of a deep understanding of basic mathematical operations.

#### A deep understanding of basic mathematical operations

In the process of learning mathematics, not all tutors will prepare the learners for deep learning. Such laxity is potent in raising mediocre mathematicians who, in most instances, cannot explain the reasoning behind a given mathematical operation. A deep understanding of mathematical operations implies the comprehension of how and why a certain mathematical operation works the way it does (Sousa, 2015, p. 56).

The gaining of a deep understanding of mathematical operations is tied in to the reasoning, cognizance of the topic, and the ability of the learner to process and store information (Sousa, 2015, pp. 49, 120). In the attempt to gain a deep understanding, various tools may be used. These include using Touch Math, and a game of dominoes. The following section describes these two in further detail.

#### Using Touch Math

Touch Math is a tool used to supplement the curriculum provided to children. Since a theoretical approach to teaching mathematics is not always efficient, the Touch Math tool takes a different approach. The tool makes use of all the senses of the learner in an intuitive manner designed to make the learning process as efficient as possible (Innovative Concepts Learning Inc., 2016). The multisensory approach adopted by the Touch Math tool is essential in the new models of learning mathematics for a younger audience. The section below explains how the Touch Math tool facilitates a deep understanding of basic mathematical operations.

#### Making use of the trademark Touch Points

Innovative Concepts Learning created and trademarked Touch Points as the tool behind the Touch Math concept. Touch Points involves the identification of points in the structural form of the numbers 1 through to 9. As the young students learn how to read, their tutor shows them the various touch points on each numeral. In a bid to enhance deeper learning and understanding, the teachers insist on their students touching and counting each touch point on each numeral.

The numeral 1 to 5 have single touch points while 6 to 9 have double touch points (Innovative Concepts Learning Inc., 2016). The Touch Points enable the learners to identify a deeper implication and meaning for numbers rather than simply identifying them as writings.

#### Establishing touching and counting patterns

A key factor in the success of Touch Points is the manner in which it engages the learners in a multi-sensorial way. Teachers show the learners trademark images and pictorial identifiers that resonate with the learners. This approach improves memorability and the acquisition of a deeper knowledge of the numerals. In addition, the touching, counting, and calling out of the numerals presents an effective approach to gaining a deeper understanding of the operations.

The choice of Touch Math to focus on counting relates to the basic tenet that most computations in mathematics are based on counting (Innovative Concepts Learning Inc., 2016). Therefore, gaining a good understanding of these basics would result in better and deeper understanding of the more complex operations…..

Enhancing Subitizing

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## Developing Computational Fluency

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### Developing Computational Fluency

Order Instructions:

Using Sousa’s (2015) premises in chapter 5:

Explain why teachers need to focus on developing computational fluency.

Describe a strategy that facilitates this important aspect of numeracy.

To illustrate your points, you may use the video Conrad Wolfram: Teaching Kids Real Math with Computers (TED Conferences, 2010). Include any additional research you have done.

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### Developing Computational Fluency

#### The need to focus on developing computational fluency.

While most learners focus on the procedural methods of solving a given problem, such a strategy is short lived in its purpose. This self-defeating approach only serves to confuse learners even more, especially once they encounter mathematical problems that require reasoning. Other problems that require a shift in operations due to a change in the presentation of the problem, or a shift in instructions are potentially problematic for such a student to handle (Sousa, 2015, pp. 112 – 113 ). To avoid such, the teachers should focus on developing the computational fluency of the learners as opposed to memorization of the process of solving a given mathematical problem at hand…..

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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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## Course Reflection and Brainstorming

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### Course Reflection and Brainstorming

Order Instructions:

This post is your opportunity to reflect on material from this course in order to gather your thoughts prior to writing your learning plan.
In 2-3 paragraphs, discuss the following:

• What were some strategies you learned during this course that you would like to incorporate in your classroom?

Thinking back to your assignment in Week 1:

• Has your view of what you need to know to teach mathematics effectively changed? If so, how? If not, why?
• Has your view of what your students need to know to be successful in mathematics changed? If so, how? If not, why?

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### Course Reflection and Brainstorming

Some information introduced in this course is relatively new to me. Case in point, the use of algorithms to increase the speed of solving complex arithmetic. The use of rapid tricks and tips for mathematics is a new concept, although one that I find very useful for future learning as well as daily activities (Julius, 1992). In addition, the fact that counting and recognition of patterns is an innate characteristic of human beings is new to me (Sousa, 2015).

These bits of knowledge have proven useful in my process of learning mathematics. In addition to new information, the course has introduced some new strategies. For me, new strategies learned include the use of subitizing and the effectiveness of connecting learning to everyday activities for both the students and the teacher….

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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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## Raising Mathematics Achievement in Your Own Classroom

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### Raising Mathematics Achievement in Your Own Classroom

ORDER INSTRUCTIONS:

Integrate what you have learned into one comprehensive plan for raising geometry and measurement achievement in your own classroom. The plan should include aspects from each week of the course and should be no longer than five pages.

o In Figure 19.2 on page 377 of Van de Walle et al. text (2013), a recommended sequence of instruction for measurement is provided.?

Reflect on your measurement instruction and the Common Core State Standards (or your state math standards).?

How will you incorporate this sequence into your own classroom instruction?

o Examine “The van Hiele Levels of Geometric Thought” (see Figure 20.1 and pages 403-406) from our text Elementary and Middle School Mathematics: Teaching Developmentally (Van deWalle et al., 2013).?

How will the van Hiele levels of geometric thought inform your planning and teaching of geometry concepts?

o Leinwand (2009) discusses ten instructional shifts to increase student achievement in Accessible Mathematics.?

Choose three instructional shifts that you would like to incorporate into your classroom.?

Why did you choose these three specific shifts?? How will you implement these shifts effectively into your own classroom? Give specific examples.