Everyone likes gum, right? Especially in school where it normally isn't allowed! A great assignment that I have came across is having students pair up to review what they have learned throughout the year while using, wait for it.... GUM. Each pair would receive a pack of gum to investigate how it can be connected to the math curriculum. You can do this through many different outlets, however I saw students completing slideshows to present to the class. It is a great way for students to review at the end of the year. Students came up with many different ideas, which is great because the possibilities are endless! A few ideas are below. - Fractions (how many pieces/how many pieces have been chewed) - Cost (how much the pack of gum was) - Division (dividing the pieces of gum evenly between class mates) - Patterning (Trident Layers) - Area/Perimeter (packaging) - Ratios (ingredients) - Time (how long taste lasts) The possibilities are endless! I experienced this activity being conquered during a supply assignment nearing the end of the year. The teacher left a movie for students to sit back and relax during the afternoon, HOWEVER.... students asked if it would be okay to watch the movie while they were working on their gum math! Students wanting to work on assignments doesn't happen very often, which obviously proved that the project was a fun one.
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What are patterning blocks?
Patterning and algebra is the mathematics strand that investigates relationships and patterns. Students are expected to “recognize, describe, and generalize patterns and to build mathematical models to simulate the behaviour of real-world phenomena that exhibit observable patterns” (Ontario Math Curriculum)
To find out more about pattering blocks and how to incorporate, not only within math lessons, but also cross curricular please don't hesitate to download my math manipulative patterning block slideshow. As an educator in the 21st century, it is crucial that students are being taught in ways that are understood and effective for their futures. Fractions affect daily lives of everyone without people even noticing. A few examples include feeding pets, driving, work schedules, laundry, baking, cooking, time management, shoe size, and financial management. Educators need to be cautious when referring to rules of mathematics and ensure there are no misconceptions or misunderstandings interpreted throughout lessons (Teaching Kids Mathematics, 36).
Fractions are not only for part-whole use, dealing with the regular circle shape. Fractions also deal with things like measurement, operator, and division. All of these different mathematical processes are very similar, however very different at the same time. “Measurement focuses on how much rather than how many parts” (Van de Walle, 285). Students need to be able to think of fractions added up as a whole rather than “dividing a pizza”. Division in schools “is often not connected to fractions…students should understand and feel comfortable” (Van de Walle, 285). Even though division is dividing certain pieces, division and fractions may become very different from one another. Researchers have also voiced their concern about not having enough emphasis dealing with operators in the curriculum. “… Just knowing how to represent fractions doesn’t mean students will know how to operate with fractions, such as when working in other areas of the curriculum where fractions occur” (Van de Walle, 285). It is important that students truly understand fractions, rather than just follow the steps. In the real world, students need to be critical thinkers as our world is full of daily situations that deal with real life fractions. Due to all of these different extents where fractions are involved, they can seem difficult to understand. It is crucial that educators take the time to explain the differences between whole numbers and fractions. When students have had the chance to understand and connect both division and fractions, they seem to have an easier time switching back and fourth between the two concepts (Van de Walle, 285). During my placement in a SK/Grade one split classroom, I quickly realized that every student learned in a different way. Lessons normally began through oral explanations and visuals, such as videos or picture books. Students would then be sent to participate in hands on activities and centers. All of these strategies necessary, however educators need to make the time to also consolidate and take up as a class what they have learned. In Ms. Klein’s class, she modeled her students’ processes on the overhead as they explained to the class how they had solved the problem (Flores and Klein, 453). “Teachers can help students see the relationship by guiding them to rewrite their answers in several ways, which will bring the connection to the forefront” (Flores and Klein, 454). A problem is easier to understand and solve when many different solutions are brought to the table, rather than having a “one answer fits all” type of approach. In class we created our own fraction manipulative, also known as a fraction kit. I believe it is important to show students how to figure out the visuals of fractions to solve problems that seem too difficult to complete. Rather than being told certain rules or steps to follow to solve the problems, Sharon let the class make an effort to problem solve on their own before taking up the answers. I believe this is important when teaching a class because students are learning through a hands-on, inquiry approach rather than a cookie cutter approach while following certain steps that they may not even particularly understand. As important as it is that students have a grasp on fractions, it is even more important that educators are able to have a stronger foundation. Teachers are now expected to teach is ways where they may have not been taught or introduced to before (Coaching for Student Success in Mathematics). It is crucial that educators become experts through collaboration with their coworkers to set inquiry goals that directly relate to their own classroom teaching (Coaching for Student Success in Mathematics). During this collaboration, educators must begin by setting planning goals and a discussion. Students must then observe students through work samples and oral descriptions to decide where to make changes. After techniques have been implemented, the educators sit down to discuss what worked and what the next steps might be (Coaching for Student Success in Mathematics). It is important to have a high-end approach that makes a difference to student learning in your classroom. Work Cited "Coaching for Student Success in Mathematics." Webcasts For Educators Coaching for Student Success in Mathematics Comments. N.p., n.d. Web. 24 Jan. 2017. “Are Rules Interfering with Children's Mathematical Understanding?”NCTM. n.d. Web. 24 Jan. 2017. Van de Walle, John., Karp, Karen., Bay-Williams, Jennifer., McGarvey, Lynn., Folk., Sandra. (2015). Elementary and Middle School Mathematics Teaching Developmentally. Toronto: Pearson. I believe it is important for educators to not provide students with the answers but instead guide them on the right path to success. Many readings from this course have encouraged this particular way of teaching; Lessons from the TIMSS Videotape Study, Strategies For Advancing Children’s Mathematical Thinking, as well as Chapter four in the text Elementary and Middle School Mathematics Teaching Developmentally.
During my personal math education, teachers would traditionally provide step-by-step instructions while students were expected to memorize formulas and complete textbook questions as quickly as possible. The article speaking about the TIMSS videotape study explains that countries like Japan have a much better success rate due to the fact that students are treated like mathematicians. The study explained how students normally have difficulties when they are being asked to learn too much at one time. In Japan, students are only given a few questions at a time to encourage “ hands on, real world mathematics, cooperative learning, and a focus on thinking” (Geist). I believe that it is important students have the chance to experience as well as experiment with math problems in as many ways as possible rather than being told what to do, step by step. When hands on experiences do not happen, students do not truly understand concepts. Van de Walle explains, “If the student forgets a step, or if there is a variation in the problem, the student becomes lost and must wait for the teacher to place him “back on track” (Van de Walle). Today’s students need be able to adapt to their surroundings and solve problems much easier than in the past. It is important to reflect on these cross-cultural differences and change the school system for the better, rather than being asked to teach more topics in less depth than teachers in Japan. To become a mathematician it is important that teachers include the following. Students must be encouraged to prove for themselves that their solutions are correct, complex problems are encouraged, and students must be able to receive satisfaction from the process (Geist). The teacher needs to emphasize unsuccessful attempts as a way of learning rather than focusing on the negative. These attempts are crucial stepping-stones to the solutions (Geist). During my future teaching practice, I will ensure that all students are able to learn what is being taught in their own unique way. It is important to understand that all students have different learning needs and there is no such thing as “one size fits all”. Fraivillig explains how important it is for teachers to encourage students to consider alternate methods when figuring out answers rather than sticking to one path. “Humans are naturally adept at learning from examples” (Fraivillig). Alternative methods are also encouraged because students will have a better understanding of a certain concept if they are able to solve it in more ways than one. Fraivillig discusses the model of Advanced Children’s Thinking, also known as ACT. There are three distinct aspects of this model. The first one includes the teacher challenging students to describe and analyze their solution methods. These explanations should be focused as most of the lesson content. Errors and efforts should be transformed into teachable moments while collaboration is valued during problem solving (Fraivillig).. The second stage is the capacity to support students’ conceptual understanding (Fraivillig). It is important for the teacher to remind students of background knowledge that connects with similar problem situations. The teacher needs to be aware of the different zones of proximal development and teach in a way to support these needs, while encouraging students to ask for support when needed (Fraivillig). The next and final step is when students’ mathematical thinking is extended (Fraivillig). A list of different solution methods should be posted on the board to promote reflection while individuals are encouraged to try the alternative methods. It is so important to engage students with the idea of a “challenge”. If students know that the teacher has maintained high standards and expectations for the class, students will think more highly of themselves and succeed further (Fraivillig). Chapter four explains that the learning through inquiry should be based on three steps. The first section occurs before the lesson, as the teacher activates students’ prior knowledge as well as establishing clear expectations while ensuring the task is understood (Van de Walle). It is important for students to connect with past schemas to ensure the math concept is understood. Teachers need to remember that students’ past experiences are what will encourage and interest them when solving problems. The second section happens during the lesson, as the teacher is encouraged to step back and allow the students’ minds to become curious, however, it is important to provide appropriate guidance along the way and provide worthwhile extensions (Van de Walle). As a teacher, it is important to step back and allow students to learn on their own terms. It is important to find the solution that fits best for them rather than being told what to do. This allows students to become more independent, rather than relying on step by step instructions. The third step occurs “after”, which is when active listening is key as well as promoting a mathematical community of learners (Van de Walle). I believe it is important that students are challenged while justifying their answers to make sense of them rather than being told how to solve questions without fully understanding “why”(Van de Walle). My math experience did not relate to this certain inquiry method at all. The teacher would teach concepts step by step and then head back to his desk where he did not want to be bothered as the students completed many questions out of the textbook. I remember one experience where I did not understand how my teacher had gotten the answer, so when I got home my Father taught me an alternative method, which I understood and completed my homework with. I was marked wrong due to the fact it was not the way that the teacher had taught. I will never forget this and I truly believe as long as a student receives the correct answer, all method should be encouraged. It is known now how collaboration between peers is very important in learning. Sharing of ideas allows students to understand a higher order of thinking and able to see that there are many different ways to solve a problem. Inquiry is key when learning in all subjects and I cannot wait until I can implement it into my own classroom. Teaching students with different needs has to be acknowledged rather than being pushed to the side like it has in the past. Work Cited Fraivillig, Judith. Strategies For Advancing Children’s Mathematical Thinking. Retrieved from https://mycourselink.lakeheadu.ca/d2l/le/content/371 59/viewContent/371672/View Geist, E. A. (2000). Lessons from the TIMSS Videotape Study. Teaching Children Mathematics, 7(3), 180. Retrieved from http://ezproxy.lakeheadu.ca/login?url=http://go.galegroup.com.ezproxy.lakehea du.ca/ps/i.do?p=AONE&sw=w&u=ocul_lakehead&v=2.1&it=r&id=GALE%7CA67379030&asid=4f9013b5af8a0bc3163f96112bb95c1c Van de Walle, John., Karp, Karen., Bay-Williams, Jennifer., McGarvey, Lynn., Folk., Sandra. (2015). Elementary and Middle School Mathematics Teaching Developmentally. Toronto: Pearson. Plot Once upon a time, in a forest far, far away there was a BIG FRIENDLY Dragon. One day the dragon decided she would go search the forest for some treasure to bring back as a surprise for her babies! So, the dragon went out and searched the forest high and low. Can you help the dragon collect all of the treasure to bring home to her babies? Materials
“The probability of an event is a measure of the chance of the event occurring” (Van de Walle, Karp, Bay-Williams, McGarvey, & Folk, 2013). There are two distinct types of probability, the known and the unknown (Van de Walle et al., 2013). This game represents both types; the “known” are the numbers that are displayed on the dice for all to see. The “unknown” are the different combinations of numbers that the two dice will create (the sum). Instructions Students will explore probability by guessing which sums (total) appear more often when they add the numbers on both die together.
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