Chapter 8 Reading

4/7/13

Chapter 8 Reading: Developing Vocabulary and Concepts

            For my Mathematics Curriculum and Instruction Course, I am beginning to create a ten-lesson plan Unit Plan. I have decided to do it on Sequences and Series, so I can teach two of the lessons to the Algebra II students at Johnson High School. Students may have worked with number patterns before, however, it is likely that this will be the first time they will have applied the technical vocabulary words such as sequences, series, iteration, summation, recursive formula, explicit formula, arithmetic (accent third syllable) sequence/series, or geometric sequences/series. I have found it challenging to figure out how to introduce these concepts in context. I want to have the students discover the definitions and have meaning to the vocabulary. In addition, I have been trying to figure out the best order to introduce the vocabulary, without introducing too much at once. There is a lot of new terminology in this unit, and I believe it is important to ensure that connections are made for students to get the most out of the material, and it doesn’t become too overwhelming.

            In other chapters of reading, we have discussed how students need to ground their reading and learning into previous knowledge, otherwise they will be unable to understand and retain the material. This same idea is developed throughout this chapter on vocabulary. The technical vocabulary from ones’ content area cannot just be pulled from a textbook and defined with other complex terminology. The vocabulary needs to be integrated with prior knowledge and allow students to make connections and remember the meanings.

            While reading this chapter, I began to question. Vacca states, “Words are labels for concepts” (Vacca, 241). However, if my students understand how to take a geometric sequence, and formulate corresponding recursive and explicit formulas, does it matter if they don’t know what they’re called? Have they mastered the objective if they can do it without saying exactly what it is? I’m not entirely sure. I feel that if they are at that level of understanding with the concepts, associating the vocabulary name with the concept is a feasible expectation. Especially because many mathematical names are given for a reason, as they allow you to make a connection to another mathematical concept. Therefore, it is important for me to facilitate those connections being made and help students to organize their grasping of concepts with vocabulary.

            A method described in the book was graphic organizers. Thus, I immediately decided to apply this to method to develop connections amongst the vocabulary that I will be using with my students at Johnson. They will be doing the unit on Sequences and Series following their unit on Probability. Unfortunately, their isn’t too strong of a correlation between the two units and it is nice to have flow and connection between units. However, I decided to map the vocabulary using a counting principle method that is frequently used in probability, which is a Tree Diagram! One can see that there are eight different types of Sequences and Series that we will be able to tackle by the end of the unit. These types are identifiable by starting reading at the red. Thus, some of the types are infinite arithmetic sequences, finite arithmetic sequences, infinite geometric sequences, finite geometric sequences, infinite arithmetic series, and so on. It is nice to have all the terms organized as well as some addition notes I added at the bottom.

           

            

           

            The text also mentions that a five minute free write on an important vocabulary word/concept can be a beneficial method to get students to start making those connections to their previous knowledge. Brainstorming is another method, in which students could work in groups and formulate a list of ideas. There are also a couple methods that emphasis the grouping and labeling of words. As I am trying to apply these methods to my lesson planning, I think some sort of grouping activity with the vocabulary may actually work well. I would maybe even integrate example sequences and series to group with the vocabulary. There are numerous examples of mapping ideas and concepts together to make vocabulary more clear. It is important to demonstrate how to effectively create these maps, and scaffold so students are able to be creative and use their own thought process, yet, know how to go about making a useful learning tool.