Technology is becoming more of an everyday phenomenon. As teachers we need to incorporate it appropriately within our classroom. You will need to find 2 activities using technology in your classroom.First, find one activity within your grade band that would be useful to help parents understand how the calculator can be used to develop mathematical concepts.
Second, find an activity that incorporates mathematics in a culturally relevant manner using mathematics appropriate for your grade band. In both descriptions, include the specific mathematical concept being covered.
Why did you select these 2 activities? What myths and fears do they address?
14 comments:
The TI Calculator Pizzle Patterns lesson is a good example of a lesson to help parents understand the uses of calculators for developing mathematical concepts. One of the suggestions is to have students use a “counting constant” where a certain number is added repeatedly by pressing the = key. I would pair this with a number chart and have students color it in (like we did in class) and find the number patterns. This is a good example because the pattern is the goal of the lesson and not the computation. If you are looking for number patterns on a chart to 100 it would take too long for many students to count by 7’s etc. to get to 100.
The other example is to show students a pattern of 4 8 12 16 ___ and have students decide what comes next in the pattern. Students can then use the same process of using the “counting constant” to continue the sequence using their calculators while marking it on a number chart.
This lesson covers addition and multiplication. This lesson covers the myth that students will not learn their basic math skills. This is giving students the opportunity to see patterns and develop their own understandings of addition and multiplication while offering students some choice (e.g. choosing the constant or developing a new number pattern to share with a classmate). They also have a chance to deal with larger numbers than they would if they were doing this strictly as mental math or through computation. This also covers the myth that students should learn the “real way” before using calculators. Students are involved in real math and are building their skills and developing patterns. Through the development of patterns students get a deeper understanding of the mathematics involved. I chose this activity because it is a wonderful way for students to create and see number patters in a very visual way. They have created their own understanding of number patterns. It has not been given to them through direct instruction.
http://education.ti.com/educationportal/activityexchange/Activity.do?aId=4940
For the second lesson, I would use the Virtual Bead Loom. I looked at a couple other sites with similar software ideas (basket weaving and Navajo rugs) but they used a full graph. The third graders in my placement are just learning about positive numbers on a graph and the Virtual Bead Loom has“beginner software” that only uses quadrant I. This lesson covers ordered pairs and geometry. I would give students a few minutes to discover on their own and then have students create a particular pattern. Students would then create a pattern and then give their design plans to another group to create. I chose this lesson because it would be a great addition to a unit on a particular American Indian Tribe where students could also create beaded patterns on an actual loom (after researching designs).
I think this covers the myth that math is just math and cannot be integrated into any topic. This is a great way to integrate a topic into every aspect of the curriculum, as we are noticing with our thematic units. This is becoming so important with high stakes testing. Otherwise, students are beginning to lose key components of education (e.g. Social Studies and Science).
http://www.ccd.rpi.edu/Eglash/csdt/na/loom/starter/index.html
Erin Barr
Natalie and Erin
The first lesson I look at was on the TI website. This lesson is titled “How do you measure up?” and is designed for the k-4 grade band. I chose this lesson specifically because Erin and I are teaching a lesson in our thematic unit on measurement and it would be a great way to have the students practice prior to the unit. This lesson has students investigate relationships between weight, height, and length through the use of balances, scales, rulers, and yardsticks. Students then use the TI-10 to find proportions and round answers to the nearest whole number. The first activity in the lesson has children compare their weight to that of the largest animal on land (the elephant). Students weigh themselves, and then enter their weight into the calculator. After entering their weight they press the FIX 10 button to round to the nearest 10. Then the question “how many of you would be needed to equal the weight of an elephant if an elephant weighed 22,000 lbs?” Students must clear their calculator, and then divide 22,0000 by their rounded weight. The next activity uses the same basic concepts except it involves multiplication. Here, students compare how much weight an ant can carry compared to its body weight (5 times) and then they use the calculator to find out how much 5 times their body weight would be. To be successful during this lesson, students must understand the proportions they are entering into the calculator. The myth and fear this lesson could possibly address is that students “should learn the “real way” before using calculators.” However, following the rules for pencil-paper computation doesn’t help students understand the ideas behind them. I think this activity can actually help develop the concept of rounding, division and multiplication in relation to measurement.
The cultural lesson I looked at was the virtual bead loom. The myth this lesson dispels is the idea that different cultures don’t have valuable mathematics concepts that can be taught to our students. This idea is completely false in that other cultures have TONS of mathematic concepts that can be used in our classrooms. The bead loom is based on “four fold” symmetry. The third graders we are working with just finished learning about symmetry, but as a culminating activity this is definitely something that we could use in our classroom. The lesson focuses on American Indian culture, and describes the mathematics behind their bead creations. The X and Y axis, ordered pairs and grids, as well as positive and negative numbers are addressed in this lesson. It is important to realize that the mathematics used in different cultures can be a fun and interesting way to introduce a concept with students.
The activity I chose that would help parents understand how calculators can be used to develop mathematical concepts deals with fractions. For third graders, basic calculators can be used as tools to help them compare fractions by converting them into decimals. For example, a teacher might ask her third grade students to find out which fraction is bigger: 2/7 or 3/8. One approach to finding this answer is by using the calculator to convert both fractions into decimals. By typing in “2÷7=” the calculator computes the division sequence and reads “0.2857142” as the answer. Typing in “3÷8=” gives the decimal “0.375”. The students will be able to see that “0.375” is bigger than “0.2857142,” a great illustration of how fractions and decimals can be equivalent. The rest of this activity involves the same process as above. Students are to convert several different fractions into decimals by using the calculator to find the bigger fraction. The last two questions ask students to make up their own fractions. Teachers can argue that the use of calculators as learning tools can help students visualize numbers in various ways. Oftentimes, fractions are difficult for youngsters to comprehend: the number “10” is bigger than the number “8” so why is 1/8 bigger than 1/10? A calculator can quickly show why this is so by converting the fractions into decimals.
For the second activity, I chose the “Alaskan Basket Weaver” activity that deals with Cartesian coordinates. The software allows students to create a virtual weave-work basket design that illustrates the important and culturally significant basket weaving of the indigenous peoples of Alaska--such as the Tlingit, Haida, and Tsimshian. Using the software to plot points on a basket-like grid, students can make up their own design by entering different x- and y-coordinate points, then creating lines or different shapes between the points.
I chose the fraction-to-decimal calculator activity because the third grade class I’m currently working with has just learned fractions. I think that this simple calculator activity can really help struggling students grasp the concept of fractions and what they represent by converting them into decimals. I chose the basket weaving activity because my students were also recently working on plotting coordinates on grid paper. By relating “plain-old math” to a real-world activity, students might be able to make more meaning out of what they’re learning. The myths and fears these two activities might address are that the calculator/software is doing the work for the students and they won’t really learn the math. Also, children might become too dependent on these tools to the point where they might forget/never learn basic math concepts.
For the calculator activity I chose Amazing Appetites. It is a great example of decoding word problems while using a calculator. I also love how it uses a children's book with the activity. This activity gets students thinking about how to make charts, number operations and sense, and to think in an algebraic sense. My cultural activity that I chose is the Navajo Rug Weaver. It incorporates how the rug is weaved from the middle out, like a graph with coordinates. I chose this activity because the third grade classroom that I am in right now is working on graphing and the coordinates of a graph. I chose the Amazing Appetites activity because it has students make charts of the information read from the book. Also the students in the classroom I am in struggle with word problems. This activity also shows that it is good to supplement word problems and chart making with a calculator. The Navajo Rug Weaver activity shows students that even simple things use math and that all cultures use math.
I found a lesson on the TI website called "Busy Hands." It has students create a cut out of hands where the fingers represent numbers. Two fingers folded down represent 2, just like counting on real fingers. The teacher then asks them, "What if you added three more? How would we write that as a number sentence?" Most students will know how to do this, but this is a chance to introduce them to the calculator function for problem solving. It allows the students to create problems with missing addends and later, missing addition or multiplication signs. I'm not actually sure that the paper cut out fingers are necessary. I think that using real fingers or even objects would be just as practical. This lesson is teaching basic algebra by making students figure out the missing addend. Students can immediately see if they were right since the calculator tells them. To the students this is basically a game but they are learning important skills. This lesson addresses the myth that calculators only provide answers and do not require students to do any of their own thinking.
For a culturally significant lesson, I selected the Navajo Rug Weaver lesson. The lesson begins by providing background information on Navajo rug weaving and the cultural significance, meanining, etc. This part of the lesson could even be taught in social studies. The math portion of the lesson teaches students how to view one of these rugs as being a series of coordinates on the cartesian grid. The very center of the rug is 0,0. Students then create their own "rug" that follows the same basic principals of symmetry. They can decide if they want their rug to be totally symmetrical or just symmetrical over the x axis or the y axis. Our class is not currently working on plotting negative coordinates, but if they create a design in the first quadrant, they could use mirrors to see what it would look like in the other quadrants. I think it is important to emphasize that their designs are not Navajo rugs, but that they were inspired by some of the patterns seen in Navajo rugs. This lesson addresses the myth that some students have that cartesian coordinates are boring and not useful in the real world. I chose this lesson because it could easily be further developed into an art lesson, giving art a practical place in the classroom where all too often, art is excluded.
Because I have not seen the students use calculators at all, or even seen a calculator in the classroom, I think the most important thing to start with is an introduction to calculators. Just because I have not seen them does not mean they don't exist, or that they have not used them sometime in the past. However, it still might have been a while since the kids have been able to use this type of technology. I found a great website with calculator games to play on the internet. The games are divided into different grade levels which would come in handy for the different levels of math learners we have. One game particularly is called “Broken Calculator”. The opening says “Eric has broken his calculator, but it might still be useful. . . “. Then you can choose the different levels you want to play, and at each level there are keys missing from the calculator and it reads “most of the keys have fallen off the calculator. You have (blank) minutes to make these eight numbers”. Since we finally got the smart board going, I thought this would be a great game we could play as a whole class. I would call on students that I believed could solve the given problem, giving everyone a chance.
My favorite cultural mathematics lesson is the Graffiti history. Being in a place where we don’t see graffiti at all, in is something the students would enjoy to learn about. I think kids would get a kick out of doing a math lesson based around an idea that is socially looked down upon. Because graffiti is almost always a case of vandalism, it would be fun to actually teach students what it is all about rather than just explaining how unacceptable it is. The site on Georgia’s delicious page lays out the history perfectly , and have some really fun games and “graffiti graphers”. This would be a really fun way to introduce graphing and the idea of coordinates and lines in the classroom.
I found a lesson about geometry using the TI that would help parents understand how students could gain knowledge of radius, diameter, and geometric shapes. In the popcorn container activity the student roll a rectangular piece of paper in two different way, long and short. They then predict how much popcorn can go in each, and if they hold the same amount. The students measure they diameter and radius by measure the radius and diameter of each cylinder. Then they take those measurements and put them into the calculator using a formula. This activity helps students develop a visual and spatial understanding of various sizes of cylinders. This will show the parents how calculators can help students understand geometric formulas and measurements.
The second lesson I chose was about teaching geometry and angles using the four directions, which are very important in Native American culture. So the students will learn different measurements of angles by breaking down the circle that the four directions are enclosed in. This lesson will also help the students relate to their Native American culture. This is how many elders use to teach math to the children. They will use protractors and various shapes in art in the lesson that again helps them relate back to their culture.
I selected these two activities because they were fun, engaging, and easy to follow. They also incorporated mathematical objectives into interesting activities. The Popcorn Cylinder activity addresses the myth that calculators cannot be beneficial to the students. The cultural lesson addresses the myth that math can only be taught in one way.
I found a calculator acitivity called “Calculator Pattern Puzzles.” The lesson is meant to allow students, K-5 to explore number patterns and relationships. For kindergartners or first graders, it can be used to introduce them to a calculator for the first time. The activity shows students how to use the “counting constant” feature of a calculator, and they are then invited to set up “pattern puzzles” for other students to solve. The lesson’s author states that the acitivity is “engrossing, and is a sure way to stimulate enthusiasm, excitement, and an appreciation for numbers.” If students become enthusiastic and excited about numbers as a result of a calculator, it would provide an excellent argument for defending their use to a skeptical parent. This lesson would address the myth that calculators can’t be used to teach mathematics, or higher-level thinking skills. When the students create their own puzzles, they must explain the strategies they use to solve the puzzles. This takes the student beyond just punching keys on their TI-108, and challenges them to create problems and answers, while also interacting with their classmates. The lesson allows for the opportunity to learn addition, subtraction, or multiplication, etc.
I found a culturally relevant lesson, which introduces students to the abacus, and how it can be used as tool for counting, and many other mathematical concepts. In this particular lesson, students should be able to demonstrate simple numbers, addition and subtraction. Students also learn historical facts associated with the abacus, and how it has been used as a mathematical tool hundreds of years. The students actually make their own abacus, so the lesson also provides some great hands-on work.
I picked the calculator activity that had to do with fractions as well (so did lindsey). The children in my classroom still seem to be struggling converting fractions and simplifying. Since this is what the student's are currently doing- I feel that a fun calculator game would be beneficial. These student's never use calculators, and I feel that they need to become more adapted in order to understand the benefits of these tools. Students are given the ability to convert fractions and decimals, all while doing it in a threat free enviornment.
I also really enjoyed the virtual bead loom page. This activty was easier to navigate then some others I encountered. Our classroom is pretty crazy, and I would need something that can operate fast. This lesson helps students understand Geometry better (which is perfect because Geometry/Geometrics were a lesson Erin and I have already taught!). This would tie into their previous knowledge as well as expand their learning styles. In our class students mostly listen to lecture and work on worksheets. This would allow for exploration and individuality. I also enjoy how it is directly related to Native American studies, allowing an intro to a new unit.
Children are afraid of math. BOTH these lessons show the child that not all math is paper and pencil. Not all math is difficult. It shows the children that math is virtually everywhere (loom) and that there are many ways to view it (calculator).
The activity that I chose and thought might be helpful for parents to understand how the calculator can be useful in developing mathematical concepts was from the geometry and measurement lessons found on the TI website titled “Map It”. In this activity students read a story, identify the locations of different places in the story, decide the distance between each set of places in the story, and create a map with a legend through the use of the TI-15 calculator. This activity will help students understand how to graph and create maps with legends on the calculator. This activity would be beneficial to parents because it will show them that calculators can be used to introduce mathematical concepts that are vital to the students’ learning and it will do so in a way that promotes student based learning.
The second activity that I chose, which incorporates mathematics in a culturally relevant way, is called "By the Numbers". In this activity, students learn about the populations of Native Americans in different states and practice reading/making a table. In this activity students will use data analysis and statistics to make a chart/table of the various populations of Native Americans in the United States. This activity allows students to use real statistics about Native American populations in an activity that will help them with the mathematical concepts of reading and making tables and charts.
I selected these activities because they incorporate math in a fun, yet educational way. I think that the two activities I chose would help get students engaged in math because they are both hands-on and different from the daily mathematics that kids are used to. The myth that many children dislike or are afraid of math would be addressed in both of these lessons, because they are interesting activities that incorporate math in an unusual way.
TI's "No More Peas, Please" is a good calculator lesson to use in the fourth grade classroom. Students are asked to find out how many peas it would take to fill a classroom or to cover their desk. It is an inquiry lesson, where the teacher provides the materials, but the students are responsible for coming up with the process to find out the answer to the question. The calculators are necessary in the lesson because the students will be dealing with numbers that are too large or difficult to compute by hand. This lesson can show parents that the calculators are useful as a tool, because they help to eliminate work that would take up a lot of time and is not completely crucial. The method the students develop to solve the problem is more important than getting the answer correct. They learn how to solve problems instead of memorizing formulas and math facts. The students must know HOW to compute volume and area before they can even use the calculators to do this.
A multicultural geometry lesson that could be used in the classroom is "Geometry and Islam." In this lesson, students learn about the geometric patterns that are evident in architecture, texts, and textiles in Islam and learn about the relevance of these patterns in the Muslim culture. The students are instructed to create Islamic patterns using paper, a compass and a straight edge. This lesson also opens the students up to realizing that geometric figures and patterns can be seen in many things outside of the math classroom.
I selected these activities because the students in my classroom are learning about similar geometry concepts. However, they solely use the textbook and worksheets. I think that activities that involved the students more, and inquiry based activities like the TI lesson would help the students learn the concepts better and understand them. The second lesson abolishes the myth that students will not need to know about math outside of the classroom. Geometry and other mathematical concepts are everywhere in the world and can be more appreciated if you understand them.
While looking at Georgia's delicious site I found a fun calculator game called "Broken Calculator". In this game the students partner up and pretend that a button on thier calculator is broke soo well say the 9 is broke. One student will say a number like 49 and the other student has to create that number on their claculator without using the number 9. So they would do 7x7 or something like that. I would probably (like Erin Barr) couple this activity with a numbers chart to help the students see the factors of numbers and patterns. I thought this game would be fun for my 4th grade class as long as they were to use multiplication or division. This would help parents to understand that we don't use calculators just to do the math for us. The students must be smarter than the calculator in this sutuation and then use the calculator as a learning tool rather than a cure all for their math ailments. :)
For my second lesson I really liked the web hunt Idea. This lesson was to get the students to look at math ideas from other countries and cultures. I thought this would be helpful to help the students understand some of the background behind math as well and broaden their understandings of other cultures. This lesson would also incorperate literacy which is obviously very important. This lesson tackles the myth that social studies and literacy can not be incorperated into math as well as to improve the students views of other cultures and the effect they have on us.
Sorry, with all the March Madness going on I forgot to post this last week, but I figured a little late is better than never so here it is. My first activity is entitled “How Do You Measure Up?” In the activity students measure weight, height, and length using balances, scales, rulers, yardsticks, and/or tape measures. Students use the calculator to find proportions and to round answers to whole numbers. Then the students use their measurements to determine how many of them would equal the size, weight, etc. of an animal such as an elephant. This lesson uses the calculator effectively because the objectives are finding the measurements, not the computational aspect of the lesson. I chose this activity because it utilizes the calculator as a tool for developing mathematical concepts. This activity helps illustrate to parents that calculators can be used as a way to enhance lessons rather than hinder them, which is a major myth/fear that parents still believe today.
The second activity was the “Virtual Bead Loom” site. This activity teaches the coordinate system using Native American bead work patterns. This website enables the students to create their own patterns using the coordinate system. I believe this would be a highly effective way to teach the subject because it allows the students to be engaged in a fun and interactive way which is preferable over direct instruction. This lesson is also important because it illustrates how Native Americans used mathematics in their everyday lives. I chose this activity because given Montana’s rich Native American history I believe this lesson could be successfully utilized in any Montana classroom.
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