Differences Between Traditional Math Instruction And A Problem Based Instructional Model

Dacey, L., & Gartland, K. (2009). Math for All: Differentiating instruction, grades 6-8. (J. Cross, Ed.) Sausalito, California, USA: Math Solutions.

In supporting the various ways students learn, educators need to introduce and share ideas that are relevant and understandable. Problem solving is generally the most challenging for students who experience difficulties in Math. Garguilo and Metcalf (2013) discuss the need for considerable scaffolding and direct instruction when it comes to real-life problem in mathematics. The student may be able to add and subtract to a satisfactory standard, but cannot apply skills in problem solving methods. These types of difficulties are usually seen in students with ADHD. (Garguilo & Metcalf, 2013, p. 360) Studies suggest using a combination of formal and informal assessment in identifying both group and individual strengths and learning by means of representing the problem in different modes; see and hear, touch,

As a student, I always enjoyed math. In high school I took all of the offered math classes, including Calculus. The first math class I took in college was a breeze, and I thought that this one would be no different. What could I learn about elementary school math that I did not already know? Contrary to my expectation, the first day of class, I learned things about math that had never been brought to my attention. This paper will discuss what I have learned about subtraction, about students, about the Common Core State Standards, and how my concept map has changed since my first draft.

For this assignment, I have chosen to study the second-grade data. By reviewing this data, I will be able to better determine where to focus my instruction as well as understand where students are at when it comes to learning math. Based on the data provided, I have decided that I will focus my instruction on two specific areas. The first area I will focus my instruction on is Number Identification. The data tells me that eight out of the seventy-four students may not understand how to successfully identify numbers. In my opinion, all students in second grade should be able to identify numbers. I will help students become successful in identifying numbers during small group instruction. This way students are provided with individual

Upon observing your class, we have learned a lot about the methods you utilize in order to help the students with mathematics and about how the students learn. Observing your class was both an honor and a learning opportunity for us, as you are an important, and well-respected faculty member in the school system. However, while we appreciate your goals and tactics to make learning mathematics easier for the students, we have discovered some flaws in the use of mnemonics, rules, and tricks for helping students understand the subject material.

| As a group students will compare their results in their practice problems and create questions for discussion.

This artifact addresses the standards of content/subject matter, diverse learners, instructional strategies, and methods of teaching in several different ways. The artifact deals with the content of 8th grade math, in this particular artifact it deals with slope, proportionality, and slope intercept form. With using these concepts, I used a variety of strategies including creative thinking and problem solving to make questions. I was also able to create opportunities for diverse learners in this lesson with the strategies and methods of the 8th grade math content. When creating this lesson it was not my goal to interconnect these four standards, it was after reflecting on the lesson that I observed I connected these four standards in my lesson

This article described the how a group of educators came together to introduce problem solving to third-grade students throughout the year as a means to teach other concepts instead of just teaching this concept when it was reached in the textbook. The educators were in groups of three with a mathematical consultant. During the course of this project the educators met with the mathematical consultant every four weeks to discuss how students responses and their presentations. During these meeting the educators would often make adjustment to better fit the students. The article contained subsections about the special spark, the before, during, and after of the problem

What is the most effective way to teach? Can students really learn and fully understand the material teachers convey to them on a day to day basis? According to a middle school mathematics teacher, his methods of teaching the traditional way was not as effective and producing a long-term impact as he would have liked. The article "Never Say Anything a Kid Can Say!" enriches us to the possibility of applying slight gradual modifications to our teaching methods and how we could find ways to utilize that information in the search for more effective teaching methods to encourage students to explain their thinking and become more deeply involved in the classroom discussions, thus developing their questioning skills (Reinhart, 2000). After

“Helping students develop mathematical dispositions in which they share their ideas, discuss others’ ideas, and so on, is always a challenge,” (The National Council of Teachers Mathematics, 2003, P. 151). I found this quote and reading to be very relatable, in the sense that students can often struggle to come up with their own ideas. This was definitely true for me and my group when we were working on the locker problem in class. In the book and in class, discussions can really benefit students and keep them engaged. “To encourage all students to contribute to discussions, the teacher should ask other students to explain their classmates ideas,” (The National Council of Teachers Mathematics, 2003, P. 153) this statement made me think of dialogic teaching. Dialogic teaching is students having a rich discussion amongst each other while being guided by the teacher. The students find out the answer on their own and the teacher does not tell them. So social norms and classroom management plays a big role when students problem solve.

Rote learning does not allow for a deeper learning of the subject being taught. This learning style makes it harder on teachers to know if their students truly understand what is being taught because the child may be able to memorize the answers and not be understanding them. “Meaningful learning involves understanding how all the pieces of an entire concept fit together.”(www.oxfordlearning.com) Meaningful learning allows children to learning and understand the topic being

Next, I observed for thirty-two hours solely in a fourth grade classroom. The mathematics time I observed in this class was spent working on problems out of a mathematics textbook. The students moved problem-by-problem and page-by-page through this textbook. Since this technique requires little to no critical thinking, it is not likely that they will recall how to solve the problems. Lastly, I spent thirty-two hours observing two sixth grade mathematics classes. The first class was students, who were performing at grade-level, and the other class was students who were performing below grade level, however both classes used the same teaching techniques. The teacher lectured, the students took notes, and then the students completed an electronic worksheet. The students then had to write their answers down on a physical piece of paper to turn in for their grade. The students were wasting time by having to copy down answers instead of learning more about mathematics. Students are not retaining what they have been taught because of the low level of critical thinking currently being used in schools.

Math lessons can be written with the influence of the arts at locations including both the target objectives as well as the learning activities. This lesson plan has students participating in these art influences to help attain mastery and retention. These activities are very important for Sousa says that teaching the arts enhances our cognitive and emotional growth (2011). The students will be experiencing the art through the visual perspective

Mary Kay Stein and Margaret Schwan Smith built mathematical tasks around the idea that the tasks used in the classroom form the basis for students’ learning. According to Stein and Smith, “a task is defined as a segment of classroom activity that is devoted to the development of a particular mathematical idea. A task can involve several related problems or extended work, up to an entire class period, on a single complex problem” (Stein & Smith, 1998, p. 269). Some tasks can be from twenty to thirty minutes long. The Mathematical Tasks Framework can be divided into three phases: “first, the task appears in curricular or instructional materials on the printed pages of textbooks,

Based on several studies, one of the best ways to understand mathematical ideas and apply these ideas is through the use of manipulatives. Students explore these manipulatives, however, it is important that they make their own observations. The teacher then should model and show how to use the materials and explain the link of these materials to the mathematical concept being taught. Schweyer (2000) stated that students learn best when they are active participants in the learning process where they are given the opportunity to explore, assimilate knowledge and discuss their discoveries.