In the article 7 Steps to High-End Learning in Teaching Children Mathematics, M. Katherine Gavin and Karen G. Moylan describe seven steps to help teachers present differentiated instruction to all students. They have been working with the National Science Foundation on Project M2 to research how this is best executed in the classroom.
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They share seven steps teachers can implement in their classroom to help differentiate instruction for all students.
1. Select an appropriate task. Since research has shown that students are able to justify thinking at high levels, begin with an advanced concept in order to allow for opportunities to differentiate and support students.
2. Increase expectations for all students. Provide concepts that will challenge all students. Allow for activities that challenge high learners and can be differentiated with scaffolding for those who may need extra support. The National Council of Teachers of Mathematics (NCTM) advocates that challenging mathematics curriculum should be provided for young students (2002). Their study found large gains from pre- to post-testing on all students and found that they significantly outscored a comparison group.
3. Facilitate class discussions about the concepts. Encourage students to justify their reasoning and generate classroom discussion in order to help students work to understand each other’s ideas and come to a conclusion on correct answers. This will allow teachers to gain insight about students thinking, any misconceptions they may hold, and in turn, allow the teacher to better differentiate instruction.
4. Encourage all students to communicate their thinking in writing. When students create written representations of their work, such as in words, pictures, or tables, they are challenged to explain their thinking in ways that others can understand. This can also allow the teacher to have insight on the students’ thought process. Teach your students to practice “writing” out their math by having group responses on a question and then have students write with partners or independently, scaffolding where needed.
5. Offer additional support. Teachers can create “hint” cards to differentiate instruction for those students who are struggling when working a problem. The card, which teachers can drop off on a desk as students work, can include a definition with a picture, a question to connect prior concepts to current ones, or a way of modifying the activity.
6. Provide extended challenges. Teachers can also create challenge cards that can be shared in the same way as hint cards, but challenges those high performing students.
7. Use formative assessment to inform instruction. Make sure to analyze students’ thinking in case instruction needs to be adjusted to correct misconceptions before giving any final assessment. Gavin and Moylan suggest using open-ended questions focusing on the essential math concepts.
They encourage teachers to start small. Pick one or two current lessons and differentiate instruction using the hint or challenge cards. After you have tried it once, reflect on how it went, and try again!
Summing it All Up
Differentiation is a way for all students to access high-level mathematics. It can easily be done in your classroom one step at a time. Check out their full article in the October issue of Teaching Children Mathematics and see examples of how they executed these steps in their research.
What are ways you have differentiated instruction for all students in your classroom?
Gavin, M. K. & Moylan, K. G. (2012). 7 steps to high-end learning. Teaching Children Mathematics, 19(3). 184 – 192.
National Council of Teachers of Mathematics (NCTM). 2000. Principles and Standards for School Mathematics. Reston, VA: NCTM.
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Hands down, one of the key take-aways agreed upon was: we need partnerships across all constituents. K-12 is beginning to talk to institutions of higher learning to find out what students need to have mastered to be successful in college; meanwhile, the institutions of higher learning are talking to companies to find out what characteristics they are looking for in employees they need to hire - this is called the STEM pipeline. The transition between kindergarten through career, or some call it, birth to career, is a holistic approach of finding out where we are losing students when it comes to proficiency in the STEM fields of science, technology, engineering and math. Statistics say students begin to mentally drop out by 5th grade and then legally drop out in 9th grade, which is just one of the many ‘leaks’ in the pipeline. The Education Policy and Leadership department of Southern Methodist University tackled this topic specifically at their 2012 annual conference