Week 2 Developing MODERN mathematics (January 23-29)

Task Discussion

• 
  Kathy Cianciola   Feb. 7, 2012, 11:24 p.m.

   

  I should have posted this a couple of weeks ago, however I just found this fun and colorful math game site today. I can't wait for my son to explore this site.  One game I found is a multiplication game called "Fruit Shoot" which involves shooting the fruit labeled with the correct answer. (Unfortunately in this particular game there is only one right answer.)  I had so much fun playing this game that if I didn't have so much to do, I might still be playing!  Another game called "Bus Driver's Math" asks the child to decide if the passengers have paid an adequate bus fare.  Different prices are posted for children, adults, and seniors, and the child is in charge of whether the person can ride the bus or not.  The math games on this sight are free, and are designed in a way that is easy to understand.  The tasks seem clear enough for children to comprehend. Don't let the look and layout of the initial page fool you.  It looks a bit boring, however all of the games I looked at had very colorful and interesting graphics. Fun, fun, fun!

  Sheppard Software (2010)

   http://www.sheppardsoftware.com/math.htm

• 
  Kathy Cianciola   Feb. 6, 2012, 7:02 p.m.

  I just found this 3-D math activity, "Marshmallow Math," when searching for math sculptures. These were made by some children who had seen other children making them, and they were looking for something to do while mom made dinner.  I thought it was interesting that they began the project independantly as a result of peer-motivation. The structure is built from marshmallows and tooth picks. This very kid-centered activity, is one that lends itself to experimentation and discovery. Children exercise patience while learning how to overcome structural challenges. They also use troubleshooting techniques to deal with structural issues while learning about geometric shapes.

  http://mathinyourfeet.blogspot.com/2012/01/marshmallow-math-solids-sculpture.html

• 
  Kathy Cianciola   Jan. 30, 2012, 10:58 a.m.

  Laura,

  I really like your clock activity.  You could even engage the students in some classroom conversation about the specific times they picked from the bag.  For instance if Betsy had 12:00, she could explain what she was doing at 12:00 such as eating lunch with her little brother etc... This would give some meaning to the idea of 12:00, making it more concrete in the child's mind. if a child picked 7:30 perhaps they were getting ready for bed, or doing their homework. they could explain this to the teacher and the class. I like the fact that it really promotes interaction, and this is also a way in which it could be considered modern.

• 
  Laura Haeberle   Jan. 29, 2012, 11:44 p.m.

   

  Objective: Teach children how to tell time using an analog clock

  (aimed at 1^st -2^nd graders)

   

  Materials: Digital Camera

  Computer

  Smartboard

  Paper bag

  Slips of paper

  Analog clock

   

  Activity:

  ·         Students will have a week to complete the activity, using the help of a parent.

  ·         During class, the teacher will write down specific times on slips of paper. All of the times will be when the children are not in school or most likely sleeping.

  ·         Each student will select a random slip from a paper bag, and is not to show their classmates what their slip is.

  ·         Then, each student will go home and look for their specific time. When they spy “their” time on an analog clock, they need to take a picture with a digital camera (either their parents’ or one borrowed from the school/teacher).

  ·         Next, they need to email their teacher the picture of the clock with their time on it (using the help of a parent).

  ·         After the week is over and each student has sent in their time, the teacher makes a slideshow of all of the clocks.

  ·         The teacher presents the slideshow on the Smartboard for the class, and asks the class to identify the time for each clock.

  ·         At the end of each slide, after the children have guessed what time it is, the teacher will ask the student who took the picture to confirm the correct time.

   

  How is this modern?

              The use of digital cameras itself is a fairly modern concept. Moreover, the ability to communicate with the teacher via email makes this lesson go more smoothly, and allow the children to learn some basics of technology. The use of the Smartboard is also key, as it allows the class to see the clocks better than with some projectors. It makes it very easy to make a slideshow, through Powerpoint. Overall, the immense amount of technology enhances the lesson, and makes it even more interactive.

   

  Standards:

  [From the Common Core Standards]

  1.MD.3. Tell and write time in hours and half-hours using analog and digital clocks.

  2.MD.7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

   

  This activity can is versatile enough for either 1^st or 2^nd graders, depending on the difficulty of the times on the slips of paper. The standards are improved because the children need to first conceptualize the time they were assigned, perhaps even drawing a picture of what it would look like. Then, they need to take a picture of their assigned time, ensuring that they know what their time is. It helps that the students are using clocks at home that their familiar with, and can gain real practice in telling time. The only limitation is that the student isn’t necessarily capable of telling time immediately, as only one time is assigned and the students are waiting for their time to occur, rather than spontaneously telling the time.

• 
  Maria Droujkova   Jan. 30, 2012, 7:11 a.m.
  In Reply To:   Laura Haeberle   Jan. 29, 2012, 11:44 p.m.

  Laura, this is a neat activity. You mention that waiting for the time is a limitation, but consider how much the student will be watching the clock to determine if the time is up yet. It's like dozens of exercises in one task. Also it will probably require the family to plan together.

  What I love about the activity is how you can extend it. For example, you can ask penpals or blogging partners from around the world to take pictures of their clocks and themselves, or their families, or their town squares with clock towers at the given time. Wouldn't it be neat to get snapshots of family or town life at "your" time, at different continents? Our Sebastian is doing projects of this sort with his student groups in India. 

  Aspects of modern elementary math I see:

  • Using technology (cameras, computers)
  • Content aggregation from many people (and you can do it with thousands online)
  • Involving families in school projects
• 
  Keisha   Jan. 29, 2012, 11:02 p.m.

  Mini Activity: What's in that bag!?

  Objectives:

  • Students will use their hands to describe the texture and shape of an object.

  Materials:

  •  Brown paper bags (that are labeled with numbers 1,2, and 3)

  • Common objects found around the classroom or in a home

  Activity:

  • Teacher starts the activity off with asking students about words used to describe how objects and things feels.

  • Teacher ask students to describe how certain shapes feels as examples for the activity.

  • The teacher splits the students into four groups and gives each group three bags with one object in each. Each group will have the same three objects in each back.

  • Every student gets a chance to feel the objects without looking into the bag.

  • The students talk among the groups to decide what words to write down to describe the objects.

  • The class will come together to discuss the words that each group wrote down and collect other words that they might have missed.

  • As a class we will try and guess what each object might be.

  • We will take each object out of the bag to see who got it right for fun.

  • Then we will compare all three objects to eachother.

  • Additional objects with different shapes and texture will be compared to the original three objects.

  Standards:

  2.6.PK.A: Use environmental objects for data collection purposes

  2.9.PK.A: Sort common 2-dimensional shapes

  2.1.PK.C: Use concrete objects, drawings, diagrams or models to combine, separate and name groups of objects

  This activity is great for all ages and can be modified in any way. It allows the students to be hands on and to use their thinking skills to come up with adjectives to describe the objects. I think this is a great way to keep students engaged. It will also get them to see how math is all around us no matter what we're looking at.

• 
  Maria Droujkova   Jan. 31, 2012, 6:36 a.m.
  In Reply To:   Keisha   Jan. 29, 2012, 11:02 p.m.

  Keisha,

  Your activity is something every kid needs to try, and many will love! It reminded me of some of the Montessori's "blindfold" tasks. I had a toy like this when I was three or four, with little polished wooden objects in a velvet bag, that I loved dearly till it got lost. As an adult, I found a similar toy in Germany. When I touched it, I just started crying - my fingers remembered the feeling so well! I had to explain what's going on to the shopkeepers, which was a challenge with my limited German and their limited English, but I now have the toy on my office table.

  Here are aspects of modern elementary mathematics I see in your activity - you have a good summary at the end:

  • Ability to modify activities to accommodate different ages and abilities
  • Hands-on work
  • Attention to student interests and engagement
  • "Math is everywhere" mindset
• 
  Carolyn   Jan. 29, 2012, 3:07 p.m.

  Mini-Activity:

  Homework assignment from the night before-collect 5-10 objects (Erasers, pencils, marbles, any nick knacks) and bring them to class in a bag. 

  That day have the students individually sorth through their items finding any patterns possible (color, shape, size).

  Activity:

  Have the students explore the room to find any other objects that may fit their categories and collaborate with other students to see how others grouped their objects. While the students are exploring have them write the objects that they find in my the room down. Come back together as a class and graph the results. Depending on age group you could have students graph their objects by themselves or as a class. Even with how you graph the objects gives flexibility. 

  To moderinize this I would use a smartboard that many classrooms are now equipped with. You can not only graph on the smartboard but as a teacher you can store your lesson plan and instructions on it.

  Standards: 

  2.1.2.B:

  Represent equivalent forms of the same number through the use of pictures and concrete objects (including penny, nickel, dime, quarter, and dollar), up to 500.

   

  The lesson plans follows this standard by graphing

   

  
  This lesson also follows all math standard accoring to Pennsylvania Departmet of Ed Standards Alligned System under section 2.6 mathematics. 

  Although this lesson follows many mathematical standards I think that the lesson also allows for creativity. The students had to bring in their own objects and come to their own conclusions about categorizing them. Ususally something like this would be preplanned with objects that the teacher has already seen. I think this is a lesson for the teacher and the students. The teacher will get to see how the students think and maybe see a pattern that they did not orginally see.

• 
  Maria Droujkova   Jan. 31, 2012, 6:49 a.m.
  In Reply To:   Carolyn   Jan. 29, 2012, 3:07 p.m.

  Carolyn,

  This is a neat activity that will allow kids to describe and share some of their familiar, probably favorite, objects. You mention using computer technology to help kids sort, and this may add some twists not possible without a computer. You already mentioned nice graphing tools, which students like to use, in my experience. Another example: a kid (or a team brainstorming together) can add objects they don't physically have to the collection by searching the Internet for pictures - for example, add volcanoes and lighthouses and anthills to the collection of cones. Activities where kids use some physical objects and some virtual objects are called "blended."

  Here are aspects of modern elementary math I see in your activity and your summary:

  • Seeing mathematics everywhere, in daily objects and activities
  • Creativity, open tasks, student discovery
  • Teacher as researcher, observing student thinking and expecting the unexpected
• 
  Kathy Cianciola   Jan. 28, 2012, 7:29 p.m.

   

  My new theme, "Letting the Child Lead," is truly in tune with my inner belief that children have an innate desire to follow their interests, and when given opportunities and options they can excel beyond our wildest expectations.  It has proven true for all five of my children, therefore I believe it is probably true for most.  This theme is very progressive, the whole idea of choices especially with regard to our vast world of technology.  This philosophy views the parent or teacher as more of a partner who guides the child along on his or her personal journey.   The surroundings should be set up to welcome interaction between the students.  Interaction in the classroom can also foster independence in learning.  This is in direct contrast with the traditional concept of the teacher instructing while the children merely sit and listen.  I found a very interesting website which supports this theme. The article speaks about "intrinsically" and "extrinsically" motivated learning.  The author explains that when a child is learning about something he finds to be of personal interest, the learning is a reward in, and of itself.  This is "intrinsic" motivation.  When a child is being told what to learn,  he is usually doing this for a grade, or for an external reward provided by someone else,  and this would be considered "extrinsic" motivation.   The article states that children are more likely to learn, and remember what they have learned if they are "intrinsically" motivated.  I don't want to over explain the article because it's really worth reading.  Here's the link:  

  http://www.nasponline.org/resources/home_school/earlychildmotiv_ho.aspx

  Example:

  We have a lot of coins at our house. Recently my son, Gil who enjoys making great discoveries, decided to dump them out all over the floor.  He then grabbed paper and crayons, and proceeded to make rubbings of the various coins.  No one ever "taught" him this but once, in the fall, we did leaf rubbings.  As soon as I noticed what he was doing, I decided to join him because it looked like fun.  Soon he began asking questions, so I realized that this might be an opportunity to share what we know about coins.  After we grouped them, and noted their various sizes and differences with respect to the fronts and backs etc,  he labeled the rubbings with the name of each coin, and the worth of each coin. This opened the door to a quite bit of conversation and discovery.

• 
  Maria Droujkova   Jan. 31, 2012, 7:44 a.m.
  In Reply To:   Kathy Cianciola   Jan. 28, 2012, 7:29 p.m.

  Kathy, we were just exploring the question of intrinsic motivation in the context of math games, in a teacher workshop in Bermuda. There are intrinsically mathematical games (like Sudoku, Set or 24) and then so-called "gamification" activities (like Jeopardy) - where the game mechanics are separate from the content. 

  Leaf or coing rubbing activity illustrates the power of REPRESENTATION for creativity and thinking. You have an object, and then you re-present it differently - in your case, with a rubbing and naming (picture and words). 

  The aspects of modern elementary math I see:

  • Letting the child lead
  • Attention to extrinsic and intrinsic aspects of learning
  • Open activities, math improvisation
  • Multiple representations
• 
  Kathy Cianciola   Jan. 31, 2012, 10 a.m.
  In Reply To:   Maria Droujkova   Jan. 31, 2012, 7:44 a.m.

  I appreciate your comments. My daughter who is now 17 years-old, really gravitated to games like soduku. She did this very independantly, and unfortunately I never even bothered to understand the concept, so I should probably do some investigation about how the game works.  In the mean-time maybe someone who has played the game could briefly explain it to me.  I suppose many of the games you mentioned are intrinsically motivated because they are done out of the desire to "play,"  but some are competitive, as well, which also qualifies as intrinsic.  Regarding the coin rubbings, my husband mentioned that this was a great activity for us, at home, but it would be difficult to carry out effectively in a room of 20+ children.  What do you think?  Sometimes I fear that when I get into a classroom that all of my fun and creative ideas will be tossed aside because they will be too difficult to execute in a large class.

• 
  SandyG   Jan. 31, 2012, 10:25 a.m.
  In Reply To:   Kathy Cianciola   Jan. 31, 2012, 10 a.m.

  Hi, Kathy.  I love Sodukus, too.  The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid contains all of the digits from 1 to 9.  The nice thing about them, is the difficulty ranges.  I've seen them used in 3rd grade classes, and I know there have been many I've thrown my hands up in defeat trying to finish. 

  You have shared some great ideas with us already, and I think you'll be surprised how they can translate to a classroom. Coin rubbing activities are also very fun in a class of 20+.  There are times when classes can go outside to the playground or explore different areas of the school such as the library, gym, or cafeteria.  It can be done as a small group exercise, with a buddy or individually.   I've recently seen this activity modified for a high school math class to be a little more 21st century by sending kids out into the school with digital cameras to find numbers or representations of them.  There were pictures of locker numbers, cinder blocks, pencils on the floor, numbers of clocks, rooms, doors and football jerseys. It was so interesting where they found all of the numbers! The students then turned their pictures into Prezis, PowerPoints, or movies in garage band.  It was a really cool project and the kids seemed to have a lot of fun!  

• 
  Maria Droujkova   Feb. 1, 2012, 7:13 a.m.
  In Reply To:   Kathy Cianciola   Jan. 31, 2012, 10 a.m.

  Kathy,

  You can be creative with group activities. Just think of what a group can do better than one person. For example, scavenger hunts work much better in groups, because different people notice different things. Another task design idea for groups is called "jig-saw" - it's when each kid's action adds to something bigger than the sum of the parts. For example, you can give each kid a paper "tile" to design using rubbings (say, in a particular color - one kid gets shades of red, another of green) and then you can make a quilt or mural out of everybody's pieces, arranging by coin value or country of origin or any other smart sorting. Speaking of "sorting' - a simple group activity we do a lot in this course is for everybody to bring (draw, write) an example, and then for the group to sort them into categories, label, etc. 

  Check out Creating and Evaluating level lists of tasks in the article "Bloom's Taxonomy Blooms Digitally" for more ideas: http://edorigami.wikispaces.com/Bloom's+Digital+Taxonomy

  

• 
  Carolyn Lesser   Jan. 27, 2012, 7:07 p.m.

   

  Mini Activity: The Magic Ruler

  Objectives:

  ·         Students will make estimates on different lengths gaining a better understanding on measurements

  ·         Students will practice measurement skills

  Materials:

  ·         SmartBoard

  ·          Paper

  ·          Pencils

  Activity:

  1.       Teacher sets up Smartboard slideshow with various objects of different lengths.

  2.       The teacher goes through all the objects and each student writes down what they think each objects length is.

  3.       Students then come up in pairs using the ruler app. to measure the objects on the screen. The ruler can move all around and become smaller and bigger in size. The students drag the ruler to make it what size they want. Students announce the measurement they found to the class and write it next to the object.

  4.       Another pair goes up to the board and picks more objects and this repeats until everyone gets a turn.

  5.       Students then compare what they wrote down in the beginning for measurements to the actual measurements they found on the board. The class discusses how close they were in their guesses and whether they think they can estimate better next time.

  How is it modern?

  This wouldn’t have been possible 20 years ago because the SmartBoard was invented in 1991 and really hasn’t been available in most classrooms until recently and still aren’t installed in some. This could have been done with actual objects and rulers but it is a good visual and hands on activity where they can create the ruler themselves and move it the way they want. It is also nice that students are able to watch their fellow classmates do the measuring on a big screen and will probably keep their attention better.

  Standards:

  This lesson follows a few standards from the Pennsylvania Standards Aligned System. For example for 3^rd grade some of the standards this lesson covers are 2.3.3.B: Identify a measurable characteristic of an object, select an appropriate standard or non-standard unit of measure and tool, and determine the measurement to a specified level of accuracy and 2.3.3.F: Estimate and verify measurements of length, area, weight, and capacity. The first standard is being covered because the students are measuring objects and choosing how to measure that object accurately. The second standard is being covered by the students because they are guessing the length of the objects then continue to actually measure the object and compare their answers. 

• 
  Maria Droujkova   Feb. 1, 2012, 7:24 a.m.
  In Reply To:   Carolyn Lesser   Jan. 27, 2012, 7:07 p.m.

  Carolyn,

  The idea of a stretchy ruler is awesome - it shows one of the key concepts behind units of measurement (namely, SCALING) in ways that allows kids to interact with it. With a computer, you can make the ruler longer keeping the same units, or you can zoom in and out and change units. You write that the screen may keep students' attention better; this may be the case, but it's still a "few-to-many" activity (two people doing, the rest watching). How about giving the rest of the class a meaningful task that would support their attention? Maybe they can record units each pair uses, or something else interesting? Or they can send images to the whiteboard?

  Aspects of modern elementary math I see in your activity and summary:

  • Dynamic, interactive links among multiple representations (stretching rulers)
  • Hands-on math
  • Visual activities
  • Students creating something themselves
• 
  SandyG   Jan. 25, 2012, 8:49 p.m.

  Mini-activity:    Spin and Dance (3^rdgrade – Special Education)

  Objective:           Student will identify numbers 1-5 by name

                                  Student will show understanding of 1:1 correspondence

  Materials:           iPad, Image Spinner app (free), Squares (or number blocks)

  Methods:

  1) Teacher will point out squares on the floor to the student

  2) Teacher will provide student with iPad with Image Spinner App open

  3) Teacher will demonstrate how to get spinner to move

  4) Teacher will ask student to identify numbers

  5) Student will activate spinner

  6) Student will speak the number that the spinner lands on

  7) Student and teacher will move the number of squares that is indicated by spinner

  8) Student and teacher will “Crazy dance” when it lands on dance

   

  Possible Modifications:

  Teacher can alter number of spinner segments and the content in the segments

  Activity can be modified to be a desk activity

  Activity can be a team exercise

  Activity can be modified to be a game and/or competition

  Activity can be modified to meet all ages/skill levels

   

  How is this activity modern?

  This activity integrates the use of technology as a fun and interactive component. The iPad was introduced by Apple on January 27, 2010.  The app used for this activity was released very recently-- January 4, 2012.    Prior to this, this activity could have been done virtually provided there was a program available on line, but certainly it wouldn’t have been possible for a child to have the technology in hand while completing the exercise.  I included a "dance" segment on my spinner because I was discussing this assignment in front of my 12 year-old son, and he thought there should be some sort of "treasure" or reward along the path of blocks. Adding something silly or fun will help hold interest and prolong the activity. My daughter is at the cognitive age that she loves silly dancing. I don't know if it's modern, but I think it does demonstrate the change in education that holds that learning that is engaging and stimulating reaches students better than lecture and notetaking.

   

  Standards:

  This activity targets several standards listed on thePennsylvania Alternate Mathematics Standards. The AMS “define the skills and strategies employed by students with the most severe cognitive disabilities who have attained proficiency in numeracy skills defined very broadly; all teachers who interact with these students will assist them in learning these skills and strategies through multiple classroom situations in all the subject areas. The Alternate Mathematics Standards also provide parents and community members with information about what students with the most severe cognitive disabilities should know and be able to do as they progress through their educational program and at graduation. With a clearly defined target provided by the standards, parents, students, educators and community members become partners in learning success” (Commonwealth of Pennsylvania, 2012).

  The standards being worked on with this activity include

  • Count using whole numbers and by 2’s, 3’s, 5’s, 10’s, 25’s and 100’s (2.1.3.A)
  • Use concrete objects to count, order and group (2.1.3.G)
  • Demonstrate an understanding of one-to-one correspondence (2.1.3.H)
  • Use whole numbers and fractions to represent quantities (2.1.3.B)

   

  Commonwealth of Pennsylvania. (2012). PASA Information. Retrieved January 2012, from Pennsylvania Department of Education: http://www.portal.state.pa.us/portal/server.pt/community/special_education/7465/pasa_information/619900

  I made a very short video of this app for you to see.  Being tired and a bit sick (she had 9 tubes of bloodwork drawn last night), my daughter was being a little uncooperative tonight, but I think you can get the idea of how it would work.

  http://youtu.be/wv1q2228pSc

• 
  Maria Droujkova   Feb. 1, 2012, 7:33 a.m.
  In Reply To:   SandyG   Jan. 25, 2012, 8:49 p.m.

  Sandy, big kudos on making a video showing how your task goes!!! For some reason, it's much more fun for kids to get their random numbers from screens than instructions with numbers from a human. I noticed that again and again. You named many extensions, and it's inspiring. I am thinking of dance as an extension of the activity; this would require a different app (we could make?) - with numbers, instead of being random, forming some shape on the floor for a dance move. Something like a square dance part, but simpler. Then kids can dance each piece, for example, form a circle and wiggle hands inside, then form a line and jump, etc. Individual pieces can be recorded on video, like you did, and put together for a whole dance. Does it make sense? I am going to ask Malke Rosenfeld of "Math in your feet" to comment - it's right up her valley! http://www.mathinyourfeet.com/

• 
  Maria Droujkova   Feb. 1, 2012, 7:35 a.m.
  In Reply To:   SandyG   Jan. 25, 2012, 8:49 p.m.

  Modern elementary math themes I see here:

  • Using computers to provide prompts (random numbers, in this case)
  • Open activities that allow modifications by ages, levels, etc.
  • Whole-body, kinesthetic math
  • Learning through play
• This comment was deleted.
• 
  SandyG   Jan. 25, 2012, 9:14 p.m.
  In Reply To:   Anonym   Jan. 24, 2012, 6:12 p.m.

  Smartboards really do add to a classroom.  Because they allow a teacher to project from their laptops, lessons are certainly more dynamic.  Unfortunately, there are many schools that simply cannot supply interactive smartboards for all of their classrooms.

• 
  Anonym   Jan. 26, 2012, 4:03 p.m.
  In Reply To:   SandyG   Jan. 25, 2012, 9:14 p.m.

  Yeah, the unfortunate thing is the expense of this technology. Those schools that can afford it, however, good for them, because yes, they are an excellant resource!

• 
  SandyG   Jan. 26, 2012, 8:50 p.m.
  In Reply To:   Anonym   Jan. 26, 2012, 4:03 p.m.

  I agree!  It's amazing how far technology has brought us.

• 
  Maria Droujkova   Feb. 1, 2012, 7:45 a.m.
  In Reply To:   Anonym   Jan. 26, 2012, 4:03 p.m.

  Check out the popular post "$2 interactive whiteboard" that describes a very affordable DIY version http://fnoschese.wordpress.com/2010/08/06/the-2-interactive-whiteboard/

• 
  Maria Droujkova   Feb. 1, 2012, 7:55 a.m.
  In Reply To:   Anonym   Jan. 24, 2012, 6:12 p.m.

  Amanda, you are making good points about technology. In terms of particular activities, which ones, do you think, are especially suitable for interactive multi-touch boards? The teacher who suggested "$2 version" (physical boards) challenges blog readers to find a single activity that can be done well ONLY on interactive technology and not on physical boards. Some things do come to my mind (e.g., zoom or 3d rotation), but I'd like to see other people's ideas too.

  I am in love with spreadsheets, and have been for years. They are a lot of fun for kids, because of the power to program and spread formulas (for example, skip-counting or doubling). I use spreadsheets any time we work with number patterns, and kids love it too.

  Here are aspects of modern elementary mathematics you bring up:

  • Attention to different types of learners (visual, kinesthetic, auditory)
  • Visualization of data (spreadsheets, graphs)
  • Data students collect on their own, and then aggregate as a class using technology