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?
11 comments:
For the activity to get parents to understand how the calculator can be used to develop mathematical concepts, I would use the Real World activities given on the TI website. There are a variety of activities that show that calculators are used in everyday life. Giving students that connection, would allow parents to see how useful calculators really are. If they are learning about jobs that use calculators in real life, than they will be learning and connecting mathematical concepts to the real world. In the Architecture activity, for instance, students would be connecting Geometry to real-life, while learning mathematical concepts using a calculator.
For the culturally relevant activity that uses mathematics, I chose was the Virtual Bead Loom. That was really cool and covered geometry and symmetry. You use the computer, with some specific software, to create your own bead patters. It educates students about American Indians, by using beads to relay information about their history and culture.
I chose these two activites because I think they are both extremely important. The first activity helps the students make connections with what their learning and the real world. That is so important, in order for them to really learn the math concepts. I picked the virtual loom because teaching students about other cultures is very important. Not only do the students get to learn about how important beading was in their culture, but they are (once again) learning important math concepts.
I think there are misconceptions because a lot of people think all you can do with calculators is "cheat". They don't see it as a problem-solving tool, or the endless possibilities technology has given us. You can do so much more with calculators now, then you could when some of these parents were in Elem. school. Our culture is using technology a lot more in the classrooms. I think it is a cool idea to use the computer, so the students can create their own symmetrical bead patterns. Allowing them to explore other outlets is crucial. Especially with technology expanding opportunity.
Michelle And Brooke
This was the lesson objective from the lesson Calculator puzzle patterns. "OBJECTIVE(s): Students will learn how to use the "counting
constant" function of the calculator, and using this function will
explore patterns and relationships with numbers, including the
concept of multiples and negative numbers. Students will
demonstrate their mastery of the function with the calculator with
the creation of "pattern puzzles" that they will share with other
students. For evaluation, all students will explain in their own
words the strategies they have discovered for solving each other's
puzzles. These pattern puzzles can be presented on level for whatever-aged group you are working with." We would explain to parents that this is an important lesson because it familiarizes the students with concepts involving addition, subtraction, multiplication, and division as well as introduces the functions of a calculator. We will have explored these same concepts with pencil and paper but showing them that the calculator is a tool providing another way to do it. The misconceptions of calculators is that they take away from the learning experience and that the children can't mentally compute.
The culturally relevant activity we chose that uses mathematics concepts was the Navajo Rug Weaver. This covered coordinates and symmetry. The activity includes an online task where the students create their own rug. This is very important to our classroom because the class uses technology in almost every lesson. This lesson teaches about the Navajo's culture and how it is influenced by the Pueblo and Spanish people discussing their spiritual beliefs. The rugs are serious and personally meaningful capturing wealth, art, beauty, and philosophy. Navajo designs are intricate and defy classification and categorization with the Cartesian grid. Using addition as well as division the rugs come out symmetrical and intricate.
The Navajo rug weaver addresses the misconception that their rugs are commodities to be sold. They are meaningful to their culture as well as reflections of mathematics and art and are taught only to the Navajo people.
I looked at the lesson, Overdue Fines, from the TI Website. This lesson incorporates word problems and simple addition, subtraction, multiplication and division. A calculator is a key tool in this activity because when the students are figuring out how much is owed to the libraries they will be dealing with decimals which can be confusing with trying to add, subtract, multiply or divide on paper. This lesson isn’t designed to teach that skill, but the skill of solving word problems and looking for the relevant information in the problem. This is why it is okay to use the calculators for the simple math. This activity would help parents see why the use of calculators are important because the worksheet is really clear through each step and ask the students to think about their answers each step of the way. This would help the parents because they would be able to clearly see that using a calculator doesn’t detract from the child’s thinking in the problem. I selected this activity because in my experience working in 5th grade the students I work with need to grasp the concept of reading closely even in math word problems because they tend to read things too quickly and/or not spend enough time trying to figure out the relevant information. I think one myth that this activity could address is that reading isn’t important in math because it is obviously very important to math problem solving.
For the cultural lesson incorporating mathematics I chose the Mangbetu design: transformational geometry. There is a short history of the culture and it shows how reflection, dilation, translation and rotation are incorporated into the design of their artwork and artifacts. It also has great photographs as examples of each of the ways the image could be changed. On that page as well are questions that would cause the students to think about potential other ways the image could have been changed (like reflected over the y-axis instead of the x-axis). It would then be a good idea to apply this idea in the classroom by having the students actually work with manipulatives and reflect them, rotate them, so forth and so on. It would be cool to even let the students make a geometric piece of artwork using these methods. I chose this lesson because I think it is a valuable lesson that would include culture and the principles or reflection, rotation, etc. I also liked how the website showed picture examples and then had questions posed of the students that required higher level/abstract thinking. One really simple but common myth this lesson would address would be that we don’t use math in the “real world”. I know a lot of students think that is true, but this would show them that even in artwork math and math concepts are used.
The lesson titled “Set Design”, take from the TI website, asks students to create a scale drawing. The set up for the problem is that the Historical Society has asked students to design a stage set as a scaled drawing of Mt. Rushmore to scale. Students are given the real life measurements of the 4 president’s faces-the height of the face, the nose length, the eye span and the mouth. They are also given help and clues regarding the proportionality of faces-“The eyes are halfway between the top of the head and the chin”. They are told the backdrop is to be 16 feet high and 24 feet wide, but their scale drawing needs to be drawn on a 12’’ x 18’’ piece of paper. This lesson is in the 5th through 8th grade category. I feel this lesson is a little advanced for the fifth grade class I’m observing, but it illustrates why calculator use is beneficial. The objective of this lesson is for students to know how to determine a scale for reducing the size of a Mt. Rushmore set. Since the objective is to determine a scale, and they are asked to show their calculations for what the full size set dimensions would be, the calculator is a useful tool, and a big reason for this is time management. This is a real-world application- Set designers do this often, and in all likelihood they use a calculator as a tool to help them determine their scale. I think this would be a good lesson to justify calculator use to parents, as students aren’t losing any math content by using a calculator, and it helps to show them a proper time to use calculators.
For the next lesson, I found a lesson from “Melting Pot Math”. This lesson deals with the flag of India. The lesson includes information about the flag, as to what it symbolizes and its history. The problems ask include lessons of proportion and scale, which is why I picked it (to tie in with the previous lesson). Questions asked include: “If the diameter of the chakra wheel was 5 inches, what would the dimensions of the flag be?”. I think if I were teaching the lesson, I would use metric measurement, as that is the unit of measurement India uses. This lesson is an example of how easy it can be to add a multi cultural component to a math lesson (addressing a myth that creating a multi cultural lesson is a time consuming process). This could be made even more of a culture exploration by investigating the ancient number systems used in the Hindu tradition.
Write number one million on the board. Ask students to pick a number that they will add repeatedly with the calculator to reach one million within reasonable class time. This teaches children about how vast and big the number one million is. I think this is a good way to explore the calculater and give students the opportunity to utilze the calculater as an aid, not just a crutch. This is a simple way to introduce math in a way that every culture can experience and utilize in a important real world activity. Although simple, it is great for students to understand the capacity of the large numbers that make our world go round.
I think the following lesson is critical for all students to be introduced to as money, like it or not, makes the world we all live in go round. As you, Geogia have proven to us, how important caluculaters are to use as a devise in the classroome, I believe thia activity supports the idea. I explored the Ti website and really thought this was a cool activity.
Use the calculator to multiply the current cost price by the inflationary factor to get the increased cost price after one year. Determine the increased cost price for each additional year [compounding inflation]
Record the data in a table
Determine the number of years it takes for the cost to double due to inflation Enter the data as a list. Set up a scatter plot of the increased cost price as a function of the number of years of inflation. Observe that the graph rises from left to right and indicates that as the number of years increases, the cost price also increases. Repeat the activity for another inflationary rate and compare the effects of the two rates of inflation.
Find the approximate number of years it takes for an item to double in cost at various inflation rates.
The following activity was also found on the Ti website and we actually exploed in class but, I just really think it is a great activity and gives students a chance to do hands on activities in a math class.
Measure the heights (cm) and the arm spans (cm) of class members.
Enter the data as lists
Find the relationship between height and arm span. Graph the data as a scatter plot. Add the graph of line y = x on the scatter plot. Observe that the data points lie very close to the line y = x. Compute the ratio of arm span to height. Predict the arm span of a person of a given height, and guess the height of an individual with a given arm span.
Both activites give students a real world connection and a chance to relate to what is around them.
An activity I found that would be useful to help parents understand how the calculator can be used to develop math concepts is “priming the numbers”. In this activity students use the fraction function of the calculator to find the prime factors of a number using the SIMP key automatically. It also shows a way for students to find the prime numbers themselves; for example if they entered 36 as a numerator and denominator and then, press SIMP and then entered a prime number they believed to be a factor. If it was a factor the calculator would reduce it and if it was not a factor the fraction would not change. So the students can guess and check for prime numbers. They can also find the complete factorization of a number.
An activity I chose that incorporates math in a culturally relevant manner is the Virtual Bead loom. I think this is a great activity for students not only does it help them master the graph, but they learn cultural background on Native American beadwork. It also shows examples of beadwork from different tribes, so students can compare and contrast the different bead work done in the various tribes. In my sixth grade class we recently did an activity that students had to know the four quadrants and be able to plot points on the graph, I think this activity would have been a great follow-up activity that would further expand their knowledge and would be fun!
I chose these two activities because they both address concepts which my sixth grade class is currently exploring. I think both activities address the myth that students will become overly dependent on the software or the calculator. But I think for both of these activities the technology is appropriate and enhances their learning.
I found an activity on UCSMP: Everyday Mathematics Center webpage that would help parents understand how the calculator can be used to develop mathematical concepts. The activity requires all players to have a calculator. They pretend that one of the number keys on the calculator is broken. One player says a number and then all players try to display that number on the calculator without using the "Broken" key. The teacher can require the students to use only division, or what ever they are working on. This activity requires students to use their computation skills in order to display the correct answer. This activity would show those parents who are concerned that the calculator is doing the math for the children that the calculator can actually be a good tool to allow students to use their brains. They are required to know how to do multiple operations, such as addition, subtraction, multiplication, and division.
The activity I found that incorporates math in a culturally relevant manner is an Alaskan Basket Weaving activity. The Alaskan Basket Weaver software allows the student to create their own basket designs. The decorative designs on the baskets are geometric. Most of these designs utilize simple geometric shapes in various combinations and patterns. The designs are also presented as being symmetrical in some way or another. Basket weaving is an important aspect of native Alaskan culture. Students would be introduced to the native Alaskan culture and geometry. This activity might be good for students who are intimidated by math, because it is not the typical math they are used to. Basket weaving is a practical skill they may be interested in. They might not even realize they doing math.
From the TI website, I found a lesson plan titled, "'Power'ful Patterns." This lesson is focused on recognizing patterns involved with exponents and repeated multiplication. Students use the calculators as a support to find the sequences of numbers that create the pattern. The lesson objective is NOT to learn how to find exponents or do multiplication, but rather to create the patterns and then recognize their relationships. For this reason, the calculators are an important tool. Doing these types of mathematics with paper and pencil can be very tedious and time consuming, and can hinder the students ability to recognize the patterns that are at the lesson's focus. When the objective is not to be able to perform the processes involved, but to make observations about them, the calculator is a tool that supports that objective and allows the students to develop the desired knowledge without distractions or unnecessary mistakes. In essence, this lesson helps to dispel the myth that the students will not learn anything by using the calculator.
The culturally relevant activity that I found was the Rhythm Wheels website based on Cuban music and sounds. This music utilizes rhythm wheels that can be arranged in various numbers of beats and with many different sound options. To use the wheels, students must set parameters of the number of beats, wheels, and "loops" (repetitions) they want. By changing the number of wheels, beats, and loops, students must be able to find least common multiples to be able to stop the wheels at the same time. They also must be aware of the different ratios that can be adjusted to match the wheels with each other, e.g., 2 loops of 4 beats with 1 loop of 8 beats. This is a great activity that helps students (and parents) to recognize that math is everywhere, even when we may not realize it. It is a good way to apply the concepts of ratios and multiples (things our 5th grade is doing right now) to real life situations, and to situations that the students might not have seen before or thought about. This lesson incorporates another culture that uses math in their everyday and significant events.
Both activities show different types of mathematics and use techniques that are outside of what the students may be used to doing every day. These types of lessons and activities are extremely important for us to use in our classrooms in order to give students a much broader understanding of the many ways math can be used and help to develop a stronger level of comfort with mathematical skills and concepts.
For activities that would connect parents and calculators I would introduce them to the TI website. On this website there are a variety of activities that are related to the real world and would spark the interest of not only the student but also the parent. By showing parents these activities you would be giving them real life concepts that would apply to them in the real world. In one particular activity (Heads UP!) the lesson revolved around probability and the calculator made the process easier. By showing the parents that calculators can make their lives easier they will begin to understand the importance of incorporating them into the school's curriculumn.
An activity that I feel incorporates culture into the mathematic field would be the virtual bead loom. During our last class I had a chance to play around on the smart board with this activity and it was really fun. This activity is extremely interactive and also shows kids the kind of bead work that is utilized in other cultures.
I chose these activities because I felt they would be an effective way for students to learn probability and graph coordinates. They are excellent lessons that get students to learn basic math concepts.
In searching for an activity that would be useful to help parents understand how the calculator can be used to develop mathematical skills I came across an activity called 'Football Scores'. I found it on the TI website and students are asked to find the different ways that a score of 77-4 in a football game could happen. This activity gives students an opportunity to work on using small math problems within a larger one. Example: if I was looking for a way to score 31 points I could score four 6-point td's, four 1-point pat's, and one 3-point field goal. With a calculator I could use parenthesis to plug in the following equation (4X6)+(4X1)+(1X3) to see if I would have 31 points. In this activity the mathematical concept being learned/practiced is using parenthesis in an equation rather than the actual simple adding/multiplying which may slow the students down too much. Spending too much time on these simple computations would shorten their time spent on the actual mathematical conceptual focus (using parenthesis appropriately within an equation). I believe this would be easy for a parent to see how a calculator can be beneficial to a student and not "cheating". Another activity in which students could use a calculator to aid their learning is called 'Reforestation'. It is also located on the TI website and students are asked to calculate how much money, how many trees after 'x' amount of years, how much area, etc. to complete a reforestation project which has certain rules that must be followed/met. Similar to the prior activity I mentioned in this post, student will use the calculator to speed up their overall strategies, not to "give them the answer". In order to do this activity correctly a student will have to apply the mathematical concepts of money, division, multiplication, subtraction, etc. to solve the problems. This is what the student are working on and not the smaller less significant multiplication/subtraction problems. The calculator will allow them to work on many reforestation problems in a timely manner rather than 1 or 2 over a long period of time. I think this would be an excellent activity for our own local culture here in Montana as deforestation/reforestation is a HUGE part of the lives of Montanans.
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