DWilson

Chapter 9 dealt with early fraction concepts.  Although students K-2 have little exposure to fractions, they are able to understand dividing a quantity so that it can be shared equally with others.  Story problems that involve "sharing tasks" give children the opportunity to use different strategies to decide how to equally distribute items.

Chapter 10 focused on algebraic reasoning.  Patterning is an important part of algebraic thinking.  K-1 students should be given many opportunities to identify and extend patterns using a variety of materials such as connecting cubes, color bears, buttons, and blocks.  Several activities were suggested, as well as the idea of using symbols such as alphabet letters to represent the structure of a pattern.  Many of my K students have been able to identify repeated patterns such as AB, ABC, ABB, or AABB.  

Information for helping students use data was covered in chapter 11.  The author stated that young children should be given many opportunities to categorize things, and several attribute activities were suggested.  I have used an activity similar to "Guess My Rule" with my kindergarten students, and they enjoy trying to figure out the classification.  I plan to use the blackline woozle cards and some of the loop activities with my students. 

Probability concepts were discussed in chapter 12.  Several interesting activities were suggested to help K-3 students build a foundation about probability.  The use of spinners, coins for tossing, and dice, are some ways to help young children with probability predictions.  I plan to use the activity "six chips" with my students.  I think it will be interesting to watch them determine where to place their chips on the gameboard, and to hear their reasoning after they have had several opportunities to play.

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Posted by: DWilson    in: My entries

Modified on January 22, 2006 at 10:40 PM

According to research, children are able to construct methods for adding and subtracting multi-digit numbers without being taught a specific strategy by teachers.  They may come up with their own strategies or share those of classmates.  The result is fewer errors, because they understand their own methods. [p.159-160]

The van Hiele levels of geometric thought are the result of research by two Dutch educators.  There are five levels:  Level 0 - visualization, Level 1 - analysis, Level 2 - informal deduction, Level 3 - deduction, and Level 4 - rigor.  Most students in K-3 fall into level 0.  At this level, there should be many opportunities for sorting and classifying - how are shapes alike and different?  The levels are sequential, but not age dependent.  There are some adults at level 0.  The classroom experiences that teachers provide are critical for children to successfully develop these levels of understanding.  The author suggests that teachers make available a rich variety of experiences with two and three dimensional shapes.[188-191]  Many activities were suggested based on the four content areas:  shapes and properties, transformations, location and visualization.  When sorting and classifying, the students should decide how to sort, not the teacher.  I plan to use activities 7.1 and 7.2, as well as geoboard activities with my students.  Suggestions were made to have stations where two or three children have access to twelve geoboards so they can compare a variety of shapes.  Geoboards can also be used to help students understand symmetry.[192-211]  I also plan to try activity 7.12 (hidden postions), with my students.  It will provide an opportunity for students to become familiar with coordinates. Pentominoes (activity7.15) is a way to encourage spatial problem solving.[213-216]

Kindergarten age children may have a difficult time understanding length measurement.  The author suggests having them start with direct comparisons of two or more lengths.  Activities 8.1 and 8.2, are ideas that I plan to try in my classroom.[228-229]

I hadn't thought much about the negative aspects of praising children, but the text suggested using comments like "I wonder what would happen if you tried" or "tell me how you figured that out", rather than  offering praise for a right answer.[cha.1]  I agree with the idea that you must begin where the children are and allow them to solve problems by using their own ideas - to approach math in a way that makes sense to them.[cha.1]  After previewing the suggested activities, I plan to use quite a few of them in my classroom:  activity 2.1 - make sets of more/less/same, activity 2.4 - up and back counting, activity 2.6- counting on with counters (this is a difficult skill for many of my students), activity 2.13 - five-frame tell-about, activity 2.14 - crazy mixed up numbers and activity 2.18 - covered parts.[cha.2]  I'm anxious to see how my students respond.  I also plan to use some heterogeneous grouping - partner those students needing help with those who are more capable.  This interaction will provide an opportunity for the sharing of ideas and strategies.[cha.1]  I am going to make better use of my hundreds chart by incorporating some ideas suggested in the book.[cha2] I thought it was interesting that some kindergarten students are more successful at solving problems than older students, because they aren't familiar with computing skills so they pay closer attention to the problem and use manipulatives to find a solution.[cha.3] 

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