Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

Teaching Strategies

Manipulatives

Fractions are an abstract concept and often confuse students because they do not work the same way as whole numbers. In primary grades, they are introduced to fractions, but they do not really manipulate them in any way, meaning they do not add them, subtract them, multiply them, or divide them. The students are expected to learn that fractions are parts of a whole.²⁰ One way to help students recognize the parts, and the size, or in the case of number lines, the length of the fractions is to use manipulatives. Kayenta Elementary is privileged in the sense that the school district provided manipulative kits, enough for each student to have their own set. Building the fractions using the manipulative kits helps students with visual concepts on which to build their fraction knowledge.

Collaboration

Our school uses Instructional Empowerment to promote student collaboration, build engaging learning cultures in classrooms to close achievement gaps.²¹ Collaboration groups have four to five students with mixed abilities. Each team member is assigned a role. In a collaborative group, one student is assigned as a Facilitator. The Facilitator’s job is to lead the discussion and keep the students on task. In addition, the Facilitator encourages team members to share ideas or questions. The group also has a Learning Monitor. The Learning Monitor helps all students understand what they are learning and encourages team members to show their work. The rest of the group are Team Members. Team Members are expected to contribute to the discussion and bring their thinking to the group. They may also step in to help the Learning Monitor and the Facilitator with coaching team members. Collaboration works for all students because they are more willing to collaborate with their peers. The team members also get an Agree/ Disagree card to aid in their discussion. The card has four parts, the students may turn the card to “Agree” to show they agree with the speaker or turn the card to “Disagree” to show that they disagree with the response of the speaker. If they have a question, they may turn to “I Have a Question” section and pose their question. The last part is “More to Add.”  If they feel like they have more to add to the discussion, they may turn the card to this section. Each section has a sentence frame to help students have a discussion respectfully.

Small Groups and Station Activities

Small group instruction is the best way to help students who are struggling. Sometimes, students just need that extra attention or extra practice. Small group instruction is pulling 3-4 students at a time with similar abilities and reteach the lesson. Another purpose for small group instruction is to reach out to all students and help them master the lessons.

While attending to students in small group instructions, the other students will rotate through four concurrent math activities. Stations are activities that review and maintain the skills already taught and allows students to refine conceptual understanding and mastery. The stations are independent practice activities to help enhance learning using various modes of learning that include kinesthetic learning, auditory learning, visual learning, and promote conversations among students. Fractions will eventually become a station activity once the students are able to confidently work with fractions.