Math Class Differentiation

I have something a little different for you all today! Usually I post my research papers, essay, and assignments from my Education program, but today I’m going to post one of my discussion posts from Instructional Practices for Math Teachers. I got 100% for this assignment, and my teacher and the students who replied to my post did not counter any of my points or have anything major to add. I know this is a lot longer than a normal discussion post, but that’s because I also combined my original post with some of the thoughts in my replies to other students’ posts.

Though this class focuses on math instruction, my intention was to come up with ideas for differentiation that can be used in any class. If you can think of any other ideas, or different ways to apply the ideas I already came up with, feel free to leave me a comment! Thanks!

Mixed Abilities Should be Celebrated!

I believe teachers should keep in mind 5 types of learning variations when differentiating lesson plans. Two were mentioned in this week’s online presentation: Learning styles and giftedness (Ackerman, 2011). First, learning styles include auditory, visual, and kinesthetic learners. Secondly, there is the giftedness of the child. I really like how Ackerman (2011) defined differentiating instruction for giftedness as “using the gifts of your students to teach them the subjects you cover.” I think too often we define gifted learners as those who find the subject matter easy, as opposed to those who are struggling, when in fact all children have at least one gift or talent (Matt. 25:14-15, New King James Version). We should differentiate instruction to incorporate the gifts and talents of both the excelling and the struggling learners.

There are a few other variations teachers must also consider. Thirdly, physical and mental disabilities. How will you accommodate and create a rich learning experience for a child with autism or one in a wheelchair? Fourth, language barriers. How will you differentiate your instruction to include students who are not fluent in English, or have speech delays? And lastly, cultural variety. Will your lesson seem foreign and out of touch to a student with a different nationality? Is there a way to incorporate the cultural variety of your classroom into your lesson plan? As teachers, we must be careful not to neglect any of these variations–learning styles, gifts, disabilities, speech, and culture–when differentiating our lesson plans.

I love how Gearhart and Saxe (2014) focused on celebrating mixed abilities in the classroom. They pointed out that, instead of being a hindrance to the learning of others, mixed abilities among students “are resources for the learning of all students in a classroom community” (p. 426). In creating my ideas for differentiated a math lesson, I first tried to keep the differentiations subtle. I agree with Tomlinson (2005) that struggling students may feel singled out and possibly inferior if too much distinction is drawn between them and other learners. I know that Ackerman (2011) stated that teachers can have the fast learners tutor the slower learners. I do not quite agree. If a teacher begins to single out certain students to give aid to other students, the children will notice and some will likely feel the sting of being the ones always receiving aid from a “smarter” student. I believe that a much better approach is to have all the students join in aiding each other, perhaps by allowing each student to explain to the class (or the person sitting next to them) a concept or method that really clicked in their understanding. I resonate with Tomlinson when she said, “Every student does some things relatively well” (para. 40). Even the struggling learners will have areas of insight that the gifted learners can benefit from. By giving all the students, and not just those who excel, the opportunity to teach and aid their fellow students, you will help all the students feel valued and intelligent, no matter their ability level.

Secondly, I tried to make these variations ones that the whole class can participate in. Every student has areas of giftedness and areas in which they struggle (Tomlinson, 2005), so I believe it is good to allow the whole class to experience variation in teaching methods.

Math topic

Data Analysis (3rd Grade). “…Interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units” (Minnesota K-12 Academic Standards in Mathematics, 2007, 3.4.4.1). “…Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets” (Grade 3 >> Measurement & Data, n.d., CCSS.Math.Content.3.MD.A.1).

Content (instruction; main lesson)

  1. State the objective for the lesson in two ways, once based on the bigger-picture view, and again incorporating the details. For example, for the benefit of big-picture learners, I could tell the class, “Today we are going to learn to make and to read data graphs.” I could then go on to give the details for the benefit of detail-oriented learners: “By the end of today you will have learned what the units on a graph mean, what different types of graphs look like and what they are best for, and how to understand what the graphs are telling us.”
  2. Have the class brainstorm reasons why the information is important to their everyday lives. For example, while discussing as a class, the children might conclude that they could use a graph to represent the data from a school-wide survey they recently conducted which reflects the varying opinions of the students about making an important change at the school.
  3. Incorporate their interests into the content examples. For whole class instruction, this could mean incorporating current school events that all the students are excited about, such as a graph showing what percentage of students performed in which talent area (singing, dancing, reciting, etc.) at the recent talent show. It would not hurt to focus on the interest of one or a few students (for example, analyzing a graph about horses if I know several students are horse-enthusiasts), but it is best to think of something that is interests the majority of the students, if possible.
  4. Write down and discuss definitions of key words. For this math topic, that could include the meanings of the different titles of graphs, as well as the meanings of the different labels and units. This will be helpful for all students, but especially those with language barriers.

Process (guided practice; learning activities)

  1. Include individual work and group work. I could break the students into groups and have each group analyze a different type of graph, but also have each student individually work on a worksheet.
  2. Incorporate manipulatives or hands-on learning for visual learners. For data analysis, I could have visual representatives for information on a graph that the children can physically sort and count to better understand what the graph is telling them. For example, if the students were analyzing a graph portraying how many family members are in each students’ family, they could sort and count little Polly-Pocket dolls to represent the family members.
  3. Seek to incorporate something fun (art, drama, music, etc.) that does not involve the mathematical side of the brain. Students could draw pictures to illustrate the data on the graphs. Or they could do a little skit showing how information on graphs is related and works together, where each child plays a different piece of information from the graph.
  4. Encourage questions! Let the students know that no question is a dumb question, and that they do not need to be afraid to voice their thoughts if they do not understand something.

Product (assessment; reinforcement activities)

  1. Provide various means for participating in whole-class discussions. I could allow students to write out their thoughts on a small whiteboard if they’re not comfortable saying them, or perhaps even illustrate their idea on the board, or pantomime it.
  2. Have each student teach another student a concept or method that they discovered or finally understood from the day’s lesson. For example, I could have the students from a group which analyzed one type of graph explain their findings to the students from another group who studied a different type of graph, and vice versa. Or, so as to not leave any student out, I could have each student share with the class (or his seatmate) one new thing that he learned about graphs from the day.
  3. Assess the students’ understanding in various ways. If I gave the students a worksheet to complete for this lesson, I would make sure it included essay questions, answers in the form of illustrations, multiple choice questions, or a mixture of something similar.
  4. Assure the children that it is okay if they make mistakes—that mistakes will only give them better understanding in the future, if they take the time to learn from them. This will keep emotionally unstable students from experiencing anxiety or escalating bad attitudes if they are not getting the right answer or understanding a certain concept.

Students who are at varying levels of understanding and ability are a resource to be celebrated! Whether gifted or struggling, they challenge, sharpen, and increase the understandings and abilities of their classmates, while their classmates return the favor for them!

References

Ackerman, B. (2011). Differentiated instruction [Presentation for Instructional Practices for Math Teachers class]. Lynchburg, VA: Liberty University.

Gearhart, M. & Saxe, G. B. (2014). Differentiated instruction in shared mathematical contexts. Teaching Children Mathematics, 20(7), 426-435.

Grade 3 >> Measurement & Data. (n.d.). Retrieved from Common Core State Standards Initiative: http://www.corestandards.org/Math/Content/3/MD/

Minnesota K-12 Academic Standards in Mathematics. (2007). Retrieved from Minnesota Department of Education: http://education.state.mn.us/MDE/EdExc/StanCurri/K-12AcademicStandards/Math/index.html

Tomlinson, C. A. (2005). How to differentiate instruction in mixed-ability classrooms (2nd ed.). Upper Saddle River, NJ: Pearson Education, Inc.

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