The authors of this article made a blunt statement that there is something missing in today’s math classes; reasoning and proof. In the past this has only been introduced and studied in high school geometry, but it has been noticed that it should be incorporated in math starting in kindergarten. Of course the rationale, support and reason will vary between kindergarten, fifth grade and twelth grade, asking students to understand why they get certain answers in math or set up a graph in that certain way is beneficial. By posing these open ended questions, students must think about the problem at hand, the answer they came up with and why it all matters. This will not engage every student who has a mental block towards math, but it will only help by relating math to real-life and putting it in different terms. This is done in a verbal or written reflection, discussion, question-and-answer, instead of this number plus this number equals this number. As teachers we try to tie subjects together, cross-curriculum. English teachers sometimes struggle with incorporating math, and visa versa. There is a fabulous way now—students can write about, create and distribute a survey, or interview each other to incorporate both language arts and math. Talking more about proving now, the article set forth examples of math problems that show contrasting answers and limitations that students can use to proof why an answer is the way it is. Two terms were defined that are important with this topic. Examples-based justification “means that students justify their generalization by stating that it worked for all the cases they tested” and structurally-based justification “which guarantees a proof”. After students worked through an activity dealing with making boxes out of toothpicks in different configurations, they contrasted the two justifications when debriefing the activity and talking about what worked and why.
Reasoning and proof is so important and needs to be re-implented for two reasons. More specifically for math, if students learn how to analyze and break down the math problems they are working with now, it will come more naturally to them later, and more generally, it is important for students to be able to research, question, test and support ideas, opinions and topics in school and the real world.

Knuth, E. J., Choppin, J. M. and Bieda, K. N. (2009). Proof: Examples and beyond. Mathematics
teaching in the middle school 15(4), 206-211.