In class, Cena seems to have a good understanding of place value and how to write a two digit number. However, when working one-on-one with a teacher, she is unable to count by 10’s and must count each block individually to come up with a total of 24. Further, she is unable to show that the 1 in 18 equals 10 even though she did show that the 8 in 18 equals 8 one’s. This tells me that she has some beginning understanding of place value but has not yet reached base ten understanding. Cena may have been able to understand the concept better and articulate it when she was not so close to the manipulation – meaning that perhaps as she watched the teacher grouping the stars, it was easier than actually grouping the blocks herself.
Jonathan had a greater understanding of place value and how you count by 10’s then count how many 1’s are left over. He has a much more developed understanding of base ten.