Know Numbers In Groups

 

As we have earlier discussed, many educators have viewed mathematics as acquiring knowledge.  This is done by possibly "stunting" development by way of  memorizing facts and processes.  A different way of viewing math is by building patterns and relationships.  This removes "a set of rules" to something a person can do with materials.  Knowledge is created by solving problems instead of acquired by of seeing and saying.

We've learned that students retain knowledge best when they manipulate, process and work with others during problem solving in mathematics.  Learning materials and manipulitives have a great impact on the students' interest in participation.  The following is a list of questions you should ask yourself before you decide on your "hands on" materials. This research has been tested by Grayson Wheatley, University of Florida.  Some source material is from his book Coming to Know Number, 1999

 - Are the goals dealing with the concepts rather than the procedures?

 - Are the BIG IDEAS being emphasized and made apparent?

- Can the students make sense of what they are learning?  Can they become responsible for their learning?

- Do these activities enhance mathematics learning?

Dr. Wheatley has several examples that enable students to envision thinking in a collection.  He uses this with dot patterns, arrays and dice.                         

A warm up game that can be used in every strand of math is called "Quick Draw"  There is a book with this title.  This photo on the left could be used for this purpose.  The photograph is laid down and covered up on the overhead.  After you have played the gamed before, all you have to say is "Quick Draw"!  The students will automatically come to attention and get ready to draw what is to be revealed.  When everyone is ready, turn on the overhead light for only two seconds.  Turn off, no talking, and students will draw what they saw.  When the heads come up, discuss what they viewed.  You'll be shocked how well your students will become at momentary viewing.  You can see that this grouping strategy with dots on a page can be ordered  in a group or disordered.  The best results is that the students soon will be able to look, momentarily, and know the number without a finger count.

                                                                                    

  Ultimately, our desire is to move the students into the tens frame.  We can show this first with the dot cards and later with the frame. It will show five connected to five.  The counting process will come so naturally as a mental process if one, two or more are missing.  With the very young students, we stay with the dots.  Ultimately, our desire is to move the students into the tens frame.  We can show this first with the dot cards and later with the frame. It will show five connected to five.  The counting process will come so naturally as a mental process if one, two or more are missing.  With the young students, we stay with the dot cards until proficiency.

 
My idea was to use dominoes to connect only those that equaled ten.  My "write-on" dice can also be used  as well as regular dice   Be sure to keep tallies for those that roll a ten! Since our number system is base ten, this is a vital foundation.