There are several NCTM process standards that are listed on the NCTM website. However, for the purpose of this blog I will only be discussing five. The first one is problem solving. According to the article, problem solving means that you are having your students participate in a task or problem where the solution is unknown in the beginning. It talks about how if students have good problem solving skills they are able to analyze the situation. This also helps them naturally become able to ask questions that are based on the situations that they encounter. You, as the teacher, play an instrumental role in helping the students develop problem solving skills according to this particular process standard. This means that the problems that you give students need to be engaging, create an environment that allows the students to experience and share their successes and failures, and discuss why the failures worked out that way. You can certainly put this into practice when teaching. An example the article gave was middle school students given different fruit juice mixtures to see which one is fruitier to introduce the topic of proportions.
The second process standard that I will talk to you about is reasoning and proof. This particular process standard is important because students need to know why a particular process or mathematical concept works. This standard is also important because this standard is used across the content areas. One of the biggest things with this standard is that it needs to be developed as the students progress throughout their school years. You can do that by having your students consistently use it in many contexts. You can implement this in your class by making sure that you are reviewing the concepts consistently all year so that they are confident and able to build on it the next school year.
The third process standard that I am going to discuss is communication. Communication is also a process standard that is important no matter what subject you are talking about but especially in math. This is because if you are not precise in your communication it will be all confusing to your students when you are explaining the concepts. This means that you need to make sure that when you are explaining a new concept to your students, or if students are explaining a justification for an answer to you, or if your students are labeling that you are correcting them if needed so they know the correct precise communication skills for math. You also need to make sure that you encourage your students to express themselves clearly and effectively especially as they get further along in school. There is also lots of benefits to your students working collaboratively together. This is because,according to the article, the students get the opportunity to see the perspectives and methods of their fellow classmates. They also,according to the article, should become more aware of their audience as they continue to get further along in their school careers. You can implement this standard into the classroom by correcting students when they are not using the correct communication. You can also implement this standard by making sure that you personally are modeling the correct communication so that your students know what to do.
The fourth process standard that I am going to discuss is connections.Connections, according to the article, is important because it helps students come to the realization that mathematics is not a set of isolated skills. It also helps kids understand that it relates in someways to the other core subjects. As the students go along in their school careers, they should, according to the article, come to expect and exploit the connections using what they have learned in one area for justification on how something does or doesn't work in another area. You also, as a teacher need to make sure that you have the connections that the students can make in their real lives as well. You can implement this standard in middle school, for example, when you have them collect graph data. This is also true in social studies. An example will be when going over measurements on a legend of a map of the united states, and you are trying to figure out which state has the biggest land area, etc.
The fifth and final process standard that I am going to discuss is representation. According to the article, this is important because it allows your students to communicate mathematical approaches, arguments, and understanding to themselves and others. It also is important because it allows students to recognize the connections that can be made between similar topics to the one they are studying, and apply those concepts to real life like situations or problems. With this particular standard, you need to make sure that you let your students represent their ideas in their own way even if it is not the standard way to do it. This is so that it makes sense to them. However, the article says that you should still teach the standard way to do it so that way that still get that opportunity to see it. You can implement this as a teacher by having the students represent a math problem such as 16-4 by drawing pictures. You can tell them a standard way to do them but don't take away points when grading if they do it differently but get the same answer.
Thanks Madison!
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