## 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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## Enhancing Subitizing Essay Paper

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### Enhancing Subitizing

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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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## Diagnosing Difficulties in Learning Mathematics

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### Diagnosing Difficulties in Learning Mathematics

Order Instructions:

In chapter 7 of the text (Sousa, 2015), seven prerequisite skills for learning mathematical concepts are described. These skills can be the key to unlocking a student’s mathematical abilities.

* 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 would you add or remove from this list? Why? See page 161 in the text (Sousa, 2015).

* How would you use these skills to diagnose and remediate a student’s difficulty with mathematics?

* You may use an example from your own classroom and insert your own, time-tested strategies.

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### Diagnosing Difficulties in Learning Mathematics

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

The type of study skills that I teach my students is the use of the SQR3 method. The method is an acronym for survey, question, read recite and review. I selected the method because it provides my students with an opportunity to ascertain the valuable ideas and facts that are present in the textbook. Moreover, they can easily note down the difficult areas that they encounter and be able to review at a later time. The process enables the students to master their content and comprehend the concepts or units that are taught in class (Palilonis and Butler, 2015).

Furthermore, the study method is segregated into three aspects before class that deals with survey and question. In addition, the second deals with after class which involves read and recite. Finally, the last one is done before the next class which is review. It provides students with an opportunity to inquire from the students or I as the instructor before we progress to the next unit (Palilonis and Butler, 2015)….

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