Through the mathematics logbook, the ways in which prior mathematical understanding and knowledge was evident in the different levels of ability from each student. Through using language to explain their understanding, the students were able to work out were they went wrong and correct it themselves thus gaining a greater understanding of the activity at hand and the mathematical concepts.
             Through talking about mathematics as well as writing encouraged deeper understanding and appeared to be an essential element to the activities and to learning mathematics. Through the communication of mathematics and talking about the activities I was provided with a valuable and deeper insight into the children's thinking and understanding. As outlined in the Principles and Standards, "communication is one of the key process standards," in mathematical learning.
             Mathematical games and other hands on activities mean that students are actively involved in their learning of mathematics and through gaining an understanding of the game they are able to gain an understanding of the mathematical content. Through actively involving the children in the activities they constructed their own mathematical meanings through their prior understanding and each others ideas and opinions.
             Through encouraging the children to make sense of the activity themselves they became excited and motivated when the concepts and ideas clicked and they openly enjoyed the mathematics. I felt that the students would have enjoyed the activity as they were in the form of games and the mathematics was not evident in all of the activities, however when discussing the activities at the end of the lesson, the understanding of the mathematical concepts that appeared in the game were all mentioned by the students themselves and they willingly and enthusiastically pointed out all the mathematics behind them.
             The open-ended activity proved to portray the necessity
             ...