DWilson

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]