Children who learn math prior to kindergarten are greatly influenced by how they learn math throughout their education (USDOE, 2008). We hear about the importance of reading to our children but the importance of building a strong mathematical foundation is not always emphasized. When many of us look back at the math concepts we learned as young children, we think of facts and procedures: addition, subtraction, multiplication, division, graphing, polling, etc. We also think of phrases that are associated with these processes such as: carry the one, line up the decimals, and invert the other fraction. What we do not always realize is that learning becomes rote without a deep understanding of concepts. For example, Why does 7×0=0? or Why did you invert the other fraction? Many students who lack numeracy skills struggle because of this lack of conceptual understanding. Strengthening the mathematical foundation by spiraling up and down the math curriculum allows students to fill the gaps in their knowledge and access higher-level math skills. The US Department of Education National Mathematics Advisory Panel (2008) reported the goal for elementary and middle school mathematics should include a logical progression from less sophisticated topics to more advanced ones, highlighting concepts and facts and procedures.
The summation of the unit is the trip to the grocery store to shop to use math strategies learned in class.
In 2014 the National Council for Teachers of Mathematics (NCTM) released “Principles to actions: Ensuring mathematical success for all” to build upon the original guiding principles of quality math instruction. In this document, NCTM emphasized that quality teaching and learning practices are essential and need to be consistent components of every math lesson. These practices include:
- establishing clear learning goals;
- implementing tasks that promote student engagement in problem solving and mathematical reasoning;
- allowing students to make connections with mathematical representations;
- having mathematical discussions to build understanding of concepts;
- asking purposeful questions that allow students to use reasoning;
- building mathematical fluency in order fo students become more skillful in procedures;
- challenging students to engage in tasks that require mathematical thought and reasoning; and
- using evidence of student thinking to assess progress toward math understanding and using this evidence to adjust instruction.
For many students with intellectual disabilities, their experience with and exposure to mathematics has been very limited. Lessons tend to focus primarily on the procedures and skills of time and money, which many teachers feel are easier to learn and more functional because they apply to daily life. They also may perceive these skills as easier to teach because they are familiar (Browder, 2006). The problem is that these skills require instruction in foundational skills that may not be easy or obvious, but are needed for students to be proficient in working with time and money. We do not often explain to students why they need to know how to count money or how knowing time will help them in life.
Let’s consider two scenarios and apply these questions based upon the teaching and learning principles of quality math instruction. Does the lesson engage students in a meaningful activity? Are the students able to connect new skills with previously learned skills? Does the lesson allow the students to use mathematical reasoning to solve a problem?
Students in Mrs. Varney’s 8th grade class go to a local grocery store on a monthly basis as part of their community-based instruction program. Mrs. Varney has predetermined the items to be purchased and divided the items among her students based upon the skills they need to learn as identified in their individualized education program. One student will need to weigh produce, two students will need to obtain a designated number of items, while another student must find a brownie mix less than $2.00.
Students in Mrs. Lusher’s 8th grade class also use grocery shopping as a community based outing. However, Mrs. Lusher’s unit spans several weeks prior to the grocery store activity. She begins the unit by introducing the idea of having a special lunch as a class. She asks her class about special events in their lives that have food associated with them (e.g., birthdays, Thanksgiving). Discussion topics also include what foods are special to them, what makes them special, etc. She spends a few days eliciting comments from her students about special occasions.
Mrs. Lusher begins the next part of the lesson by challenging her students with the statement, “I’ve decided that for our special class luncheon we are going to prepare brussel sprouts and beets.” Most students let her know that they do not like her choices. Then, she then facilitates a discussion about when it is important to have a choice and what is the best way to make a class decision. This discussion leads to the activity of voting, polling, and graphing.
Once the students have reached a decision on the lunch menu, she explains that the class will be divided into two equal teams to prepare the meal, one for the main course and one for dessert. The class offers strategies for dividing up the class (e.g., boy/girl, counting, color of hair). Each group is given a recipe and directed to determine the amount, type of ingredients, and the approximate cost needed to feed the entire class. Mrs. Lusher and her paraprofessional assist each group of students depending on their skill level. The summation of the unit is the trip to the grocery store to shop, to use math strategies learned in class, and to follow recipes to prepare the luncheon.
Going back to the previous questions, even though both lessons engage the students in a meaningful activity and provide instruction on necessary math skills, Mrs. Lusher’s students are given the opportunity to apply problem solving skills and connect previously learned knowledge with new skills. Her students are more likely to apply the principles of polling, graphing, counting, and measuring in future activities.
As you prepare your math lessons this year, keep these questions in mind. Are your math lessons providing your students with concrete opportunities? Do your lessons promote reasoning and problem solving? Do you pose questions to your students that will promote meaningful discussion? Do you build conceptual understanding of concepts as they relate to the students lives and experiences? A positive response to these questions will help your students build a stronger foundation in their conceptual understanding of mathematical reasoning.
Browder, D.M. & Spooner, F. (2006). Teaching language arts, math, and science to students with significant cognitive disabilities. Baltimore: Paul H. Brookes Publishing Co., Inc.
National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. Retrieved from Executive Summary http://www.nctm.org/uploadedFiles/Standards_and_Focal_Points/Principles_to_Action/PtAExecutiveSummary.pdf
National Mathematics Advisory Panel. (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education: Washington, DC. Retrieved from: http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf