Algebra Tiles and the FOIL Method
Algebra is one of the most critical classes a mathematics student takes. In this crucial course, the student must make the jump from concrete numbers and operations to variables and uncertainty. Unfortunately, this area of mathematics is where most students lose interest in mathematics because the concepts become too abstract. The abstractness frightens students and this fear is where the typical “I hate math” attitude comes from. Educators need to be aware of this problem and accept that the traditional methods of teaching mathematics, specifically algebra, are too focused on intangible concepts. These concepts need to be introduced to students in a more approachable manner, such as concrete representations. One such concrete representation, algebra tiles, is an excellent way to introduce the concept of multiplying monomials and binomials. The multiplication of monomials and binomials is an essential ability for students to master in order to continue mathematics. Many students are intimidated by the concept of multiplying these vague terms with variables. In essence, the traditional method of teaching the multiplication of monomials and binomials, the FOIL method, is too theoretical for students to comprehend. A new approach must be used, and algebra tiles are one of the best new ways to approach this topic.
To start, the traditional FOIL method needs to be studied. The Math Help tutoring website explains the FOIL method as the process of “multiplying the terms in parentheses to get the quadratic form.” FOIL is an abbreviation for the order a student follows when multiplying. “FOIL, of course, means: First, Outside, Inside, Last – the order of multiplication to expand the dou...
... middle of paper ...
...iplying monomials and binomials. However, if one method must be selected, algebra tiles are the best way to address the needs of today’s mathematics students.
Works Cited
Leitze, Annette Ricks, and Nancy A. Kitt. “Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts.” Mathematics Teacher. 93.6 (2000) : 462-466.
Otken, Phil. “The Foil Method.” Technical Tutoring, 2004. 24 November 2004.
http://www.hyperad.com/tutoring/math/algebra/The%20FOIL%20method.html.
Stein, Mary Kay, Margaret Schwan Smith, Marjorie A. Henningsen, and Edward A. Silver. Implementing Standards-Based Mathematics Instruction. Columbia University: Teachers College Press, 2000.
Wilcox, Ted. “Using the Foil Method.” Free Math Help, 2004. 24 November 2004.
http://www.freemathhelp.com/using-foil.html.
Wiliam, D. (2007). Keeping learning on track: classroom assessment and the regulation of learning. In: Lester FK (ed) Second handbook of mathematics teaching and learning. Information Age Publishing, Greenwich, pp 1051–1098
Politics and laws are one of the biggest factors keeping gay and lesbian couples from adopting children. This is to discourage or prevent gay and lesbians from even trying to adopt. It has been proven that m...
“How stern the power of Almighty God who crushes sinners with such righteous blows(Canto XXIV lines 109-110)!” In Dante’s Inferno, Dante Alighieri describes a trip through Hell, visiting the various sinners and circles of Hell. Dante also uses many experiences and beliefs from his real life to enrich his views of Hell and his idea of Divine Punishment. Dante’s perception of Divine Justice includes sinners whom he places in Hell for committing crimes without regret, they are placed lower in Hell according to the severity of their sins. Dante is not always just in his placement of sinners, his personal grudges and archaic Catholic beliefs get in the way of true Divine Justice.
Japan is a very homogenous society made up of about 98% ethnic Japanese. They tend to put a lot of emphasis on family and communities, and value the group more than the individual (Aliasis, 2013). The social hierarchy important and members of the society are expected to conform. One way is showing respect for one’s elders, for example the oldest member of a group is served first and their drinks are poured for them (AngloINFO, 2014). This mentality is common in the business world as well. Promotions are usually based on seniority and people often work at one company their entire lives. This way of life brings satisfaction and pride to the people (Aliasis, 2013). When greeting others it is customary to bow, although the Japanese are familiar with our ways and would expect us to want to shake hands rather than bow (Bazzel, 2013; Angloinfo, 2014). Also, being too direct about what one is really thinking is not socially acceptable. The Japanese use subtle language and rely heavily on non-verbal forms of communication (Aliasis, 2013).
Homosexual parents exhibit parenting capabilities equal to and sometimes better than heterosexual parents because in most cases they plan to become parents and are already stable. Research shows that the children of homosexual couples are on the same level as children from heterosexual parents in a variety of life-success measures. “…a psychologist at Clark University in Massachusetts who researches gay and lesbian parenting. Gays and lesbians rarely become parents by accident, compared with an almost 50 percent accidental pregnancy rate among heterosexuals, Goldberg said. "That translates to greater commitment on average and more involvement."And while research indicates that kids of gay parents show few differences inachievement, mental health, social functioning and other measures, these kids may have the advantage of open-mindedness, tolerance and role models for equitable relationships, according to some research.” (Pappas) People opposing same-sex parenting have assumptions that these children will suffer socially, mentally, and emot...
The Inferno is a very captivating narrative poem by the poet Dante which describes his imaginary journey towards finding God after falling asleep in the middle of his real life journey. The relationship between God and man is depicted clearly in The Inferno, The Divine Comedy. It is clearly shown that God does not associate with the evil or those in between good and evil. Though we see that God has hope for some who were once lost but can be redeemed and he sends his angels to guide those who get lost trying to find their way like Dante (Auerbach, Erich, 1961).In this significant journey, Dante first encounters a dark place in the woods and is guided by the shade of Virgil who appears to him in the woods. Dante says,
Children can enhance their understanding of difficult addition and subtraction problems, when they learn to recognize how the combination of two or more numbers demonstrate a total (Fuson, Clements, & Beckmann, 2011). As students advance from Kindergarten through second grade they learn various strategies to solve addition and subtraction problems. The methods can be summarize into three distinctive categories called count all, count on, and recompose (Fuson, Clements, & Beckmann, 2011). The strategies vary faintly in simplicity and application. I will demonstrate how students can apply the count all, count on, and recompose strategies to solve addition and subtraction problems involving many levels of difficulty.
Families headed by gay and lesbian parents are just as diverse as families led by heterosexual couples (Thompson 36). The only difference in these families is there are two mothers or two fathers. They are seen as “unnatural” by most conservatives and religious organizations and their affiliates (Gateway Child Wellfare Information). The media usually portrays same-sex couples as “white, middle-class, two-parent families who have been together for many years. In actuality, these families are a small percent of the larger LGBTQ family community”. Because of the cultural and societal views of what makes an “ideal family” in the United States as “one mother, one father, and two children,” it is difficult for others to accept those that have two mothers or two fathers. These families are usually started by one parent who “came out” as lesbian or gay after divorcing a husband or wife. Additionally, blended families, which consist of one parent who remarried and the step-parent adopted the child or children that way, through artificial insemination and surrogacy, and there are couples who adopt children from the foster care system and adoption agencies (Thompso...
“Class,” I announced, “today I will teach you a simpler method to find the greatest common factor and the least common multiple of a set of numbers.” In fifth grade, my teacher asked if anyone had any other methods to find the greatest common factor of two numbers. I volunteered, and soon the entire class, and teacher, was using my method to solve problems. Teaching my class as a fifth grader inspired me to teach others how important math and science is. These days, I enjoy helping my friends with their math homework, knowing that I am helping them understand the concept and improve their grades.
Mathematical dialogue within the classroom has been argued to be effective and a ‘necessary’ tool for children’s development in terms of errors and misconceptions. It has been mentioned how dialogue can broaden the children’s perception of the topic, provides useful opportunities to develop meaningful understandings and proves a good assessment tool. The NNS (1999) states that better numeracy standards occur when children are expected to use correct mathematical vocabulary and explain mathematical ideas. In addition to this, teachers are expected
...l preference, and cognitive development have been tracked for these children into adulthood. Study after study have asked different questions in attempts to find similarities and differences in children raised in these two different family structures, but scientific consensus shows that there are no noticeable differences in children brought up by a gay or lesbian couple.
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
Silver, E. A. (1998). Improving Mathematics in Middle School: Lessons from TIMSS and Related Research, US Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328.
...S. and Stepelman, J. (2010). Teaching Secondary Mathematics: Techniques and Enrichment Units. 8th Ed. Merrill Prentice Hall. Upper Saddle River, NJ.
Throughout out this semester, I’ve had the opportunity to gain a better understanding when it comes to teaching Mathematics in the classroom. During the course of this semester, EDEL 440 has showed my classmates and myself the appropriate ways mathematics can be taught in an elementary classroom and how the students in the classroom may retrieve the information. During my years of school, mathematics has been my favorite subject. Over the years, math has challenged me on so many different levels. Having the opportunity to see the appropriate ways math should be taught in an Elementary classroom has giving me a