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?
10 comments:
I found a fun activity from one of Willowdale Elemetary’s links. The activity is entitled “Farm Stand Math.” This activities’ objective is basic computation in an every day environment: grocery shopping! The game gives you a scenario in each round of play, which you must answer and type into the calculator. For example, it may ask how much 4 eggs and 2 apples cost at a rate of 4 cents per egg and 1 cent per apple.
If I were to play this game with my class, I would set-up a “real-life” situation within the classroom, as opposed to playing the computer game. I would ask students to crate a shopping list of the items that they need and estimate the total cost, prior to shopping. Next, after the students had chosen all of the items that they wished to purchase, (there would be a 5-item limit) students would add the final total cost of their groceries with paper and pencil. Finally, the students would cross check their sums by typing in each item’s price in a calculator. The calculator simply serves as a tool to check their answers before “checking out.”
I would go on to explain that many adults use calculators each day as well. They use them in situations ranging from balancing a checkbook, to planning family vacations. I think that this activity utilizes calculators, while not detracting from the students’ personal computing abilities. This also may help students to notice (if they made a mistake) where in their personal computation processes that mistake occurred. The site that this activity can be found at is: http://www.prongo.com/farm/game.html
In light of this year’s Olympic games n Beijing, I found two activities that could be used to incorporate China into math activities within the classroom. First, I would introduce the abacus. Yes, I know that I am working with second graders, but a basic introduction, explanation of its uses and student exploration may be kept appropriate.
After a brief history, students would explore counting with an abacus, which would include counting, regrouping and understanding of new operations. We would also have a weeklong Chinese chess unit. Chinese chess is very similar to western chess, though uses only 5 pawns, two “guards” instead of a queen, an elephant instead of bishops, and rules limiting the King and his guards to a 3x3 grid (the fortress or palace). This activity covers the mathematical concepts of counting, estimating, addition, multiplication and subtraction.
I selected the “market” activity because it is practical and engaging. I also chose it because it uses the calculator as a follow-up learning and cross checking tool. I chose the abacus and chess activities because, due to the Olympics, they are contemporarily appropriate and engaging as well. The abacus is a historically important tool used not just in China, but Europe as well. Many extensions and integrations could be done with this activity. No myths or fears were mentioned throughout my research of these activities, nor am I currently aware of any now.
I decided to explore the TI site some more and see what activities other teachers have come up with for kindergarten/first grade use. I found a couple, but one that jumped out at me was dealing with place value, since our class just finished up working with place value not too long ago. This activity has the students working in groups of 3 or 4 and the teacher reads out a large number, (or smaller if the class has only covered up to the “hundreds place”) then after the students have written the full number down the teacher tells student A to put in the first number by saying enter “3 thousands” then the student B adds “5 hundreds” and hands the calculator to student C and so on… The students are then able to see how the different components add up to create their number. To make it more challenging the teacher can have the students enter the numbers in any order…so do “3 thousands”, then “7 ten thousands”, then “6 ones”, and then “5 hundreds”, so that the students can really grasp where exactly each place value is. I believe this activity gives students another way to visualize/conceptualize what place value means. I believe even the most anti-calculator parents would see the value of using the calculators in this manner to help students discover place value!
My second activity I found under Dr. Cobb’s Ethnomathematics webquest which has many different mathematics topics in many different areas. After going to the webquest I found the Mankala link, a game that I always loved to play growing up. I think Mancala is a game that works well with almost any age group, because the game gets more challenging as the students’ strategy increases. I think it would be interesting to research and discuss with the class where Mancala originated (Africa) and how it came to be. This Mankala link allows the students to play by themselves on the computer; there may even be a way to play against another student on the computer, but I have yet to explore the site fully. As I still enjoy this game today I believe it is a way to engage students’ lifetime interest.
As for the myths and fears, the first activity dispels the myth that the “calculators give kids the answer” because in that activity there really was no “answer.” The calculator does not tell the kids which place value is which; it just allows the students to see the correlation between when they put in the number and where it “goes.” I also liked this activity because students were not working towards an answer but more just working with the numbers and being able to see the place value relationships in what we say and how we write it. As for the second activity, I chose it mostly because I remember it as a child and I like the fact that it is now on a computer as well. I feel that most students still do not get enough “computer” time when in the school; most classrooms I have seen give students maybe one hour a week working with computers. Many of the students are getting most of their computer experience at home, but those that do not have computer access are going to end up behind their peers in understanding technology, so any time I can find an appropriate computer based counterpart to an activity or lesson I will allow my students to use it.
One activity I found that would be practical in explaining to parents how calculators can be useful in the development of mathematical concepts is from Texas Instruments called Number and Operation Sense: Whole Numbers. The concept of this activity is to understand number and operations, gain fluency in arithmetic computation and to develop number sense. I chose this activity because it allowed students to work with calculators to develop an understanding of number operations. Students attempt to come up with a number expression between the numbers 1-12 using 1,2,3 and 4 and one or more of the four operations, x, ÷, +, and –. For example
3+4x 2+1=12. Students can manipulate the calculator to understand order of operations. First they can try the expression above on a calculator that recognizes order of operations and one that does not. Without knowing this they can discover that order of operations affects they outcome of an answer! This is a great opportunity for students to manipulate these numbers, which will make it easier for them to remember and understand the importance of the order because of this simple activity.
This activity addresses the fear that calculators are used only for computations which is not true, they can also be used to see patterns and to understand that the calculator is only as smart as the operant.
The second activity I chose is called Pre-Colombian Pyramids and the concept is to gain an understanding of geometric shapes and how they can be made into symmetrical figures such as pyramids. I selected this tutorial because it allows students to use technology and at the same time discover mathematics while learning about another culture. Students get the opportunity to use a computer and learn how pyramids were built by the Mayan. They also get to learn about symmetry and how it is was beneficial in making pyramids along with how many levels were used and approximate amounts of blocks in each level. Students answer questions about the shapes they see, beginning with simple pyramids and moving to more complex.
The fear this tutorial addresses is that technology can be used to benefit students learning if used appropriately. Students are not playing video games on computers they are learning mathematical concepts. Computers are a huge part of everyday life and if students begin early they will be better at using them and understand how they can use them to their benefit!
This is Chris and Kylie!
Lesson 1:
After exploring the Texas Instrument website we found an activity titled How Do You Measure
Up? This activity begins by reading a story to the students’ and then reviewing the information in the story. In Activity 2, the class compares the difference in weight from an elephant to an average adult male. After discovering the two weights, they are entered into the calculator. The calculator in this lesson is used as a tool to help students round to the nearest 10’s place. We think this is a great lesson for parents to recognize how calculators can be implemented into the classroom. The calculators in this case are not giving the children answers, they are guiding them in discovering how to round numbers correctly.
We would explain to parents the importance of the calculator in this lesson because it helps guide students discovery of mathematical concepts. In the second grade classroom we are observing at, the students have been introduced to comparing numbers, as well as rounding numbers to the nearest 10. This would be a great activity that could incorporate both of the concepts.
Lesson 2
An activity that incorporates mathematics in a culturally relevant manner could be the virtual bead loom. Although graphing would probably be a bit too advanced for our students, this was the best I could find and it might be a good way to introduce to them the idea of graphing. There is a part on the website where you can look at “starter software” and you can use this page to make graphs. The “starter software” keeps the graph in the first quadrant so then you don’t have to worry about explaining negative numbers to students. It could be a good website to use to introduce students to the ideas of graphs and one of the many different types of graphs (scatterplot). You could allow the students to play around with this website and make their own designs using the different colored beads and placing them in various locations on the graph by typing in the place they want the bead placed in an ordered pair. This website is good too because it gives some cultural information behind why Bead Looms are important to American Indians.
I have chosen the activity that we worked with in class in terms of students learning their math facts. I would show students how to set their calculators to practice addition problems and then have them go through as many as possible in a given amount of time. I would have students write down which problems were giving them difficulties during the calculator activity, so that I could spend more time (and the parents could spend more time) in helping the child with certain problems. Then as an additional activity using the same program, I would have children see how many they could do in a minute. Students can scroll upwards on their calculator to see how many they have answered. Students could write the numbers down, chart them, and see if improvements have been made in speed of mathematical facts. I would not grade these, but it would give me an idea of where students were in using a calculator to solve addition problems. This activity can also been done in the first grade using subtraction problems. Problem solving and numerations are the key concepts in all of these activities.
The activity that incorporates mathematics in a culturally relevant manner that I have chosen for the first grade is Mancala (or sometimes called Mankala). It is an African game that was played 3000 years ago in Egypt, and is still played around the world today. The game has several versions to it, and with the first grade I would begin with the basic version. This game has children counting stones, marbles, or seeds and placing them in seven pits -- six playing pits plus one score pit, the Kalaha -- per player. At the beginning of the game, each of the (12) playing pits contains 3 seeds (or beads or stones or balls or whatever). Students take turns placing seeds into the pits in a counter-clockwise manner. Seeds falling into the Kahala receive points. Although this game seems a bit difficult to explain on paper, I have played it and know that first graders could grasp the concept. With Mancala, children can see a concrete game in front of them to learn the rules, and then play it on the computer. I have found two sights that have Mancala. Both sights allow for change of rules depending on age (or ability). This game can help children with counting (numerations), problem solving, and connections (from math to real life). In addition, it is a fun way for children to learn math!
I have chosen both of these activities because they address the same mathematical concepts in two completely different ways. Children who learn in a variety of ways tend to be more successful learners. Coming from a teacher who is technologically illiterate, I can see that there is advantages to teaching children with technology and that children are more apt to learn if they are engaged in the lesson being taught.
Well, I just now looked up at the rest of the comments AFTER I posted and Julia and I apparently sharing a brain. Go figure!
In mathematics education today, there is a growing awareness that
children need experience with problem-solving, math instruction can be inquiry-based, and the use of calculators should be introduced and applied at every level. The lesson I found was designed to allow young children to explore number patterns and relationships while introducing them to the calculator at the same time. The lesson was designed for K-5 students, but seems to work best in grades 1-3. I have come to notice that children are highly motivated by the use of calculators.
To use as an inquiry-based lesson, you may want to rely on the students own "discoveries" to generate the questions and explorations. In the lesson I found it is recommended that a classroom set of calculators be used. Texas Instruments TI-108 works well even with Kindergarteners. Students participating in this activity will learn how to use the "counting constant" function of the calculator, and using this function will explore patterns and relationships with numbers.
The teacher will introduce the idea of the "counting constant" and demonstrate how to make the calculator count. This varies from calculator to calculator, but is usually based on the following simple code: punch 1+1= then continue to punch the = button continually to have the calculator count sequentially. By changing the "code" students will be able to begin to explore patterns, i.e. 2+2=, 6+6=, 100+100=, etc. The same works for subtraction, starting say at 100-1=, or 100-5=. Let the students explore and then present what number patterns and relationships they found. Next Model for students a pattern puzzle such as: 4, 8, 12, 16, ____what comes next? Or, 24, 28, 32, ____, 40, ____, 48, ____? Fill in the missing numbers. For more advanced students you could try a puzzle such as 0, 6, ____, 18, 24, ____, 36, 42, ____, 54, 60. These pattern puzzles can be presented on level for whatever age group you are working with. At the end of the lesson, give students the opportunity to explain their strategies for solving the pattern puzzles, either using the calculator and the counting constant function, or pencil and paper, or their heads. You should get an excellent idea of where each child stands with number concept and/or place value. To allow further exploration and extensions as well as calculator practice, set up as an independent math lab activity. Post pattern puzzles
for viewing and allow other students to attempt to solve.
The next activity that I found was based on the Yup'ik native Alaskans. This tribe has navigated the tundra for centuries using a combination of mathematics and environmental information. The website I found provides the opportunity to explore some of the indigenous navigation techniques of the Yup'ik. I specifically would use the Tunturyuk Time activity in my classroom. In the Yup'ik native Alaskan tribe the word Tunturyuk represents the Big Dipper Constellation. This activity might be a little advanced for my students, but with the right amount of support I think it would be a great activity. The Tunturyuk Time activity generates a random position of Tunturyuk for a specific month, and asks you to use this information to determine the time of day, just as the true Yup’ik navigators would. With this activity students can play individually or as a class. To play as a class you need 15 chips (or markers) worth 1 point each, and five chips worth five points each. Starting with the youngest player you go from student to student asking for the correct time that is shown on the computer or smart board. If a student gets it correct they get a chip. If a students answers incorrectly the questions moves to the next student. Play continues around the room until there are no chips left. I really liked this activity because it shows how another culture determines what time of day it is.
Both of the lessons I discussed seem to be great interactive activities that would work great in the current classroom I am working with. I like the calculator activity because it addresses the myth that calculators should never be used in the classroom, and that the calculators make students lazy. This activity shows how the calculator can be used as a very beneficial tool with young students in helping them recognize number patters. It is also a great way for a teacher to show parents how calculators can benefit a students understanding of a math concept. Having an activity like this can help teachers get over the fear of addressing parent concerns with using calculators.
I chose the Tunturyuk Time activity because I think it is very important for students to understand that there are many ways that math can be used outside of the classroom. The students in my class are learning how we tell time right now. I think it would be a great real life connection to see the way a different culture tells time. I think this activity helps to address the myths students may have heard about other cultures, and see how beneficial it can be to learn another cultures ways. I feel that both activities are great asset and will become an important part of my future classroom. This blog really opened my eyes to many different ways of teaching math that I will definitely take with me into my teaching career.
In mathematics education today, there is a growing awareness that
children need experience with problem-solving, math instruction can be inquiry-based, and the use of calculators should be introduced and applied at every level. The lesson I found was designed to allow young children to explore number patterns and relationships while introducing them to the calculator at the same time. The lesson was designed for K-5 students, but seems to work best in grades 1-3. I have come to notice that children are highly motivated by the use of calculators.
To use as an inquiry-based lesson, you may want to rely on the students own "discoveries" to generate the questions and explorations. In the lesson I found it is recommended that a classroom set of calculators be used. Texas Instruments TI-108 works well even with Kindergarteners. Students participating in this activity will learn how to use the "counting constant" function of the calculator, and using this function will explore patterns and relationships with numbers.
The teacher will introduce the idea of the "counting constant" and demonstrate how to make the calculator count. This varies from calculator to calculator, but is usually based on the following simple code: punch 1+1= then continue to punch the = button continually to have the calculator count sequentially. By changing the "code" students will be able to begin to explore patterns, i.e. 2+2=, 6+6=, 100+100=, etc. The same works for subtraction, starting say at 100-1=, or 100-5=. Let the students explore and then present what number patterns and relationships they found. Next Model for students a pattern puzzle such as: 4, 8, 12, 16, ____what comes next? Or, 24, 28, 32, ____, 40, ____, 48, ____? Fill in the missing numbers. For more advanced students you could try a puzzle such as 0, 6, ____, 18, 24, ____, 36, 42, ____, 54, 60. These pattern puzzles can be presented on level for whatever age group you are working with. At the end of the lesson, give students the opportunity to explain their strategies for solving the pattern puzzles, either using the calculator and the counting constant function, or pencil and paper, or their heads. You should get an excellent idea of where each child stands with number concept and/or place value. To allow further exploration and extensions as well as calculator practice, set up as an independent math lab activity. Post pattern puzzles
for viewing and allow other students to attempt to solve.
The next activity that I found was based on the Yup'ik native Alaskans. This tribe has navigated the tundra for centuries using a combination of mathematics and environmental information. The website I found provides the opportunity to explore some of the indigenous navigation techniques of the Yup'ik. I specifically would use the Tunturyuk Time activity in my classroom. In the Yup'ik native Alaskan tribe the word Tunturyuk represents the Big Dipper Constellation. This activity might be a little advanced for my students, but with the right amount of support I think it would be a great activity. The Tunturyuk Time activity generates a random position of Tunturyuk for a specific month, and asks you to use this information to determine the time of day, just as the true Yup’ik navigators would. With this activity students can play individually or as a class. To play as a class you need 15 chips (or markers) worth 1 point each, and five chips worth five points each. Starting with the youngest player you go from student to student asking for the correct time that is shown on the computer or smart board. If a student gets it correct they get a chip. If a students answers incorrectly the questions moves to the next student. Play continues around the room until there are no chips left. I really liked this activity because it shows how another culture determines what time of day it is.
Both of the lessons I discussed seem to be great interactive activities that would work great in the current classroom I am working with. I like the calculator activity because it addresses the myth that calculators should never be used in the classroom, and that the calculators make students lazy. This activity shows how the calculator can be used as a very beneficial tool with young students in helping them recognize number patters. It is also a great way for a teacher to show parents how calculators can benefit a students understanding of a math concept. Having an activity like this can help teachers get over the fear of addressing parent concerns with using calculators.
I chose the Tunturyuk Time activity because I think it is very important for students to understand that there are many ways that math can be used outside of the classroom. The students in my class are learning how we tell time right now. I think it would be a great real life connection to see the way a different culture tells time. I think this activity helps to address the myths students may have heard about other cultures, and see how beneficial it can be to learn another cultures ways. I feel that both activities are great asset and will become an important part of my future classroom. This blog really opened my eyes to many different ways of teaching math that I will definitely take with me into my teaching career.
The first lesson that I found is from the Everyday Mathematics website. It’s a calculator game called “Broken Calculator” designed to help students with addition and subtraction problems. If you were in a higher grade band and/or depending on where your students were at, you could incorporate division and multiplication etc. The way that it works is that each student is split up into a group or pair (however you decide) with each player having their own calculator. Next, one player says a number. All the players then try to get that number displayed in some way on their calculator without using the “broken” key. For instance say the “broken” key was 25 each individual student could get the calculator to display the number 25 by:
5 + 5 + 5 + 5 + 5 =
24 + 1=
30 – 5 =
This wasn’t part of the lesson, but to make it even more fun I think you could have the students each come up with their own equations within a designated amount of time and at the end, share their answers. For every equation a student had that the others in the group (or whoever they were playing against) didn’t have they would receive a point. I think this would get them to further engage in thinking of trickier equations. I also think that this lesson with or without the competition part, would be fun for every child. It’s a fun and engaging game that would help students learn and build on their addition and subtraction skills.
The 2nd lesson that I found incorporates mathematics in a culturally relevant manner. It is called the Virtual Bead Loom. This website provides some cultural information on Native American beadwork and its mathematical concepts. The software on this site allows students to simulate traditional loom designs so that they can create new designs on their own. Some designs are far more complex than others, but it allows you to chose guides for which one you’d like to complete. Also, it allows you to pick points and it tells you the cordinance of where you should set your geometrical shapes. This is a fun activity to show younger students the geometric shapes you can use to create an overall design while incorporating a Native American tie-in. This is a great technological way to incorporate math, in a way that is not just a video game or something of that nature that some people might automatically assume since it involves the computer.
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