Teaching math can be a daunting task, especially in the lower grades. Teaching mathematical concepts through lecture and paper and pencil work isn’t enough to achieve deep understanding, math reasoning or problem solving skills. Math manipulatives are “hands on” or virtual materials designed to engage students in active investigation to gain higher levels of understanding. Manipulatives not only allow students to explore concepts, but also allow teachers to see what students are thinking. “The National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics emphasizes the importance of using manipulatives and visual representations, as well as mathematical modeling, in each of its standards at all grade levels” (Shaw, 2002). The use of manipulatives in the classroom are also supported by educational theory. Jean Piaget’s theory of cognitive development indicates that elementary school students are typically in the concrete operational stage of cognitive development. This stage encompasses the development of organized rational thought. Students begin to develop the abilities of conservation and reversibility. Although students are able to approach problems in a logical way, they typically struggle with thinking abstractly or hypothetically (McLeod, 2010). Manipulatives are an excellent way to bridge the gap. Students are able to work with materials to create concrete experiences which help lead to abstract reasoning. Mathematic manipulatives…
zero. In the new system the order of the number mattered since for example, twenty-five is completely different than fifty-two. The position of each digit was significant, therefore zero was needed to get digits into their correct places. For example, writing two thousand and five required two zeroes in order for two to be in the thousand place value, and five in the ones place value and there are no numbers in the tens and hundreds place value [11]. German bankers and Italian merchants took…
In fourth grade various new math ideas are presented and many students can face difficulties when new material is introduced. Difficulties are especially displayed when it comes to discovering decimals. Although decimals are introduced in fourth grade they are continuously presented in math thereafter. One common misconception held about decimals is the idea that the more digits that are presented in a number, the greater the value of the number. An example of this is students believing that 3…
Part B Diagnostic Assessment During the diagnostic assessment which focused on grade three student, Boris’s comprehension of number placement and value, Boris did well in most areas, with minimal exceptions. Boris took a great deal of time, when requested to partition the double digit the number. Though they progressed to partitioning the larger numbers in a standard and acceptable non-standard manner, they answered the two digit partitioning question with various multiplication equations.…
Persuasion is a constant and rather successful method of getting people to do certain things. We are constantly being influenced and also influencing other people around us. There are several principles that help explain why humans sometimes irrationally do certain things that they wouldn’t normally do. Three of this several principles include the paradox of choice (which proves that when giving a lot of choice for any particular item, satisfaction decreases and sales decreases), scarcity (which…
Data Type Description and example use **You must provide an example of what each data type could be used for** String A data type used in programmings such as an integer and floating point unit, but is used to represent text rather than numbers. • I bought 3 CD’s which were from 3 different artists. It shows that I bought it from 3 different people. • If (Option 1==Option 2) If the values are the same, then it is true. If they are different, then it is false. • Usernames are an example of…
The Maya was an ancient civilization renowned for their remarkable architecture as well as their exceptional knowledge in astronomy and mathematics (Peterson and Haug 2005, 322). Reaching their population peak around 750 A.D, the Maya experienced societal collapse between 750 and 950 A.D (Peterson and Haug 2005, 322), the cause of the collapse remaining a heavily debated topic today by archaeologists. This essay will argue that the primary contributing factor of the Maya collapse was drought;…
Development of place value Place value and the ten-base system are important foundations of later mathematical concepts. The development of these concepts takes years and is built upon pre-number and early number development. Therefore, the development of place value and understanding of the ten-base system needs to be understood in relation to early concepts. Classifying and patterning are elements of pre-number development that need to be developed as part of numeracy. Classifying helps…
Henrik Ibsen’s play, “A Doll’s House” depicted the life of Nora and the events that unfold around her. This play was far ahead of its period, breaking new waters that have never been seen before. Although the play was controversial for its time, in this era it is seen as a revolutionary piece, not only for playwriting, but for the rights of women and the right for individual freedom. The events that unravel throughout the play lead to the conclusion that Nora’s decision portrayed in “A Doll’s…
This summer I built the classic puzzle game Bejeweled, and abstract strategy games English Draughts and Chess. I did this because I am a big fan of all three of these games, and I wanted to challenge myself by implementing the game logic. Also during the summer I started learning android. The app that I built that I am most proud of is a calculator that works in sixty different numeral systems from base 2 to base 62. I started the project making a calculator that uses hexadecimal instead of…