Here is my final assignment for Instructional Practices for Math Teachers. I must say, I had a very nice final’s week (which is unusual). I told my family that it was probably the most stress-free finals week I had ever had! I think it was due, first of all, to the fact that I did not do any subbing that week, and thus could focus mainly on my studies, and secondly to the fact that my teacher gave me a light load for the final week–very unusual at Liberty University. I am used to having my final week be the hardest, most loaded week of the term! Anyway, I had plenty of time to devote to this final paper, in which I was to choose one question from a list to answer in a 4-5 page essay with at least 5 scholarly sources. I ended up having 11.
My teacher gave me 98% on this paper. She agreed wholeheartedly with all the points I made, and did not explain the 2% dock, so I’m assuming it was for some minor grammar/spelling error(s). One other thing she mentioned that I thought was interesting is that she is capable of doing just what I recommended–she can teach any area of middle school math without a textbook!
Keep on reading to find out why this is so impressive and important….
Textbooks: Worth & Limitations
Question: What are some of the advantages and disadvantages of teaching mathematics without a textbook?
Every teacher dreams of being a super-teacher. Young education majors hope to be the teacher who always is planning engaging lessons, incorporating hands-on, differentiated activities, and teaching in new, innovative ways—never succumbing to boring lectures or lengthy homework assignments from a textbook. Mathematics teachers are no exception, especially when “in some of [their] education classes, [they] may be encouraged to set textbooks aside” (Kauchak & Eggen, 2014, p. 292). It can be an appealing thought to throw out textbooks altogether and teach mathematics from a new standpoint, one that focuses on creativity, logical thinking and construction of learning, and personal discovery of knowledge. There are a number of advantages and disadvantages of removing textbooks from mathematics education; however, taking a balanced position is far superior to the extreme position of disbanding their use altogether.
The advantages of removing reliance on math textbooks are numerous. First, comprising a lesson plan without textbooks raises the standard for teachers by requiring more from them. They must have a thorough grasp of the information they will be presenting to their students. They cannot leave it to the textbook to instill proper technical terminology and methods. Neither can they fall back on a textbook to present to students a well-illustrated, interesting lesson. Many students are not enthusiastic about studying math because their teachers are equally unenthusiastic. Ridener and Fritzer (2004) stated that many teachers dislike the study of mathematics. As a remedy, they recommended that teachers become more familiar with the subject to “build teacher confidence” and “translate into teacher, and subsequently, student enthusiasm” (Ridener & Fritzer, 2004, p. ix). The quality of mathematics instruction would be greatly improved if teachers would become familiar enough with the material that they are capable of teaching it without textbooks, whether they do so or not.
Secondly, by taking the focus off of textbooks, teachers are better able to focus on the needs of each child. Their lessons can become more differentiated. Instead of following a specific procedure outlined in a textbook, students can move through the learning process at their own pace. Teachers can also increase students’ appreciation for math by teaching with a real-world perspective not limited to textbooks. Mathematics is essentially the study of logic, reasoning, and patterns (Ridener & Fritzer, 2004). It should be taught as such; as White (1903) said, “While the children and youth gain a knowledge of facts from teachers and textbooks, let them learn to draw lessons and discern truth for themselves” (p. 119). Some teachers have used problem-solving approaches to mathematics instruction with great success among students, measured by increased enthusiasm for participation (Reinhart, 2000) and improved test scores (Carroll, 1998). In Reinhart’s (2000) case, this approach included using effective questions, classroom discussions, and hands-on activities as a replacement for the traditional math lecture and homework assignment. Some students are scared enough of the abstract concepts of math (Ruffins, 2007) without adding the fear of struggling through a textbook filled with mathematical terminology.
Lastly, discarding textbooks in the mathematics classroom allows their place to be taken by a richer literature base. Charlotte Mason, “a British reformer and pioneer in the field of education” (Carroll & Carroll, n.d., para. 1) believed that students should study “living books” (para. 1)—primary sources written by individuals who were passionate about their topic, and thus have much better chance of evoking the same passion in the readers—instead of textbooks, which are secondary sources compiled by those who feel an obligation to cover the most territory in the least amount of space. Many teachers have begun incorporating a richer literature base into the mathematics classroom by introducing math concepts with fun, brightly illustrated children’s books (Nelson, 2012). There is an even more serious side to this discussion. Some textbooks actually create a “superficial understanding or even faulty ideas” of mathematical concepts (Kauchak & Eggen, 2014, p. 292). Apparently, “very few mathematics education researchers have taken a really close look at what is in the textbooks, with the focus on how the material is presented and what kind of learning may be implied” (Kajander & Lovric, 2009, p. 174). This adds even more weight to the arguments for avoiding textbooks in the mathematics instructional plan.
There are potential setbacks to completely removing textbooks from the math curriculum. First, the wealth of information found in textbooks will be missing. Kauchak and Eggen (2014) highlighted this fact. Textbooks offer teachers well laid out plans for scope and sequence. They pointed out that textbooks have a wide range of information, which can be picked and chosen from based on the needs of the students and the school. If teachers are not careful, studies created without the framework of textbooks can become narrow and important knowledge points can be missed. Kauchak and Eggen (2014) further explained that many textbooks nowadays contain ideas for teaching in accordance with state standards. Teachers will miss out on these and other supports textbooks offer if they throw out their use altogether. Consequently, teachers who refuse to utilize textbooks will need more time to prepare lessons. They must make sure that they become well-versed in the content before presenting it, as they cannot fall back on assigning a reading in the textbook. It is common knowledge that teachers have very little extra time on their hands. Furthermore, students will need to learn the discipline of using textbooks in order to be prepared for college and the workforce. It seems that textbooks can prove very beneficial and should have a place in the classroom.
There is a balance between the two extremes of letting textbooks become the sole educators in the classroom and throwing them out altogether. A much better option is to put textbooks back into their proper perspective. In order to do so, one must understand their worth in the classroom, as well as their limitations. For example, textbooks can never do the work of the teacher (Kauchak & Eggen, 2014). Teachers should refrain from the temptation to use math texts in place of personal instruction. Teachers have the ability to incorporate biblical concepts and spiritual applications catering to their individual students into the study of mathematics that factual, inanimate textbooks are incapable of. Teachers should also keep in mind that it is unhealthful for developing children to spend too much of their day passively poring over textbooks—they bodies as well as their brains must be kept active (White, 1923).
On the other hand, textbooks are an excellent resource—usually very broad in scope with little bias. Practical ideas for incorporating a balanced use of textbooks into mathematics education include using the Bible and nature as primary textbooks. Both are revelations of God, and both can be used to discuss and teach mathematical concepts. Another idea is to replace hard copy textbooks with digital ones, which have self-refining tracking and engaging, interactive pages (Patton & Roschelle, 2008). Lastly, teachers can use textbooks in the preparation of their lesson plans in order to gain good ideas and broaden their content horizons, but then go on to present the lesson to their students in their own format, with their own creativity and with the particular needs of their students in mind.
Advantages of teaching math without a textbook include a more rigorous standard of content knowledge placed upon teachers, a more creative, differentiated classroom atmosphere for students, and a broader incorporation of literature. Potential setbacks include the loss of the framework and ideas from textbooks for mathematics lesson planning, which, naturally, will require more preparation time from teachers. In light of this, a balanced view of textbooks is far better, where one understands their value and can use them appropriately. An experienced teacher of 14 years explained that, though it might be appealing to write creative lessons all the time and teach the students directly from personal knowledge and primary sources, realistically one must realize that there will be days when the well of creativity will run dry or time will run out to prepare and present a lesson properly (M. Westmore, personal communication, February 13th, 2015). Textbooks should not be allowed to rule the classroom and instruction, but neither should they be discarded altogether.
Carroll, J. & Carroll S. (n.d.) Charlotte Mason. Retrieved from Living Books Curriculum: http://www.livingbookscurriculum.com/charlotte-mason
Carroll, W. M. (1998). Geometric knowledge of middle school students in a reform-based mathematics curriculum. School Science and Mathematics, 98(4), 188-197. doi:10.1111/j.1949-8594.1998.tb17415.x
Kajander, A. & Lovric, M. (2009). Mathematics textbooks and their potential role in supporting misconceptions. International Journal of Mathematical Education in Science and Technology, 40(2), 173-181. doi:10.1080/00207390701691558
Kauchak, D. & Eggen, P. (2014). Introduction to teaching: Becoming a professional [5th ed.]. Upper Saddle River, NJ: Pearson Education.
Nelson, C. (2012). A math-box tale. Teaching Children Mathematics, 18(7), 418-425. doi:10.5951/teacchilmath.18.7.0418
Patton, C. M., & Roschelle, J. (2008). Why the best math curriculum won’t be a textbook. Education Week. pp. 32-24. Retrieved from Academic Search Premier.
Reinhart, S. (2000). Never say anything a kid can say! Mathematics Teaching in the Middle School, 5(8), 478-483. Retrieved from http://www.jstor.org/stable/41180868
Ridener, B. & Fritzer, P. (2004). Mathematics content for elementary and middle school teachers. Boston, MA: Pearson Education, Inc.
Ruffins, P. (2007). A real fear. Diverse Issues in Higher Education, 24(2), 17-19.
White, E. G. (1903). Education. Mountain View, CA: Pacific Press Publishing Association.
White, E. G. (1923). Fundamentals of Christian education. Nashville, TN: Southern Publishing Association.