June 10th Articles

Rich Activities

Teachers should be sure to plan rich activities into their lesson plans. We must consider our students grade, age, prior knowledge, and experiences when considering rich activities. The expectations of each class will very, so planning is very important. Another thing that must be considered when planning rich activities is the cognitive demand. This MUST be higher level. The four cognitive demands include: memorization, procedures without connections to concepts or meaning, procedures with concept or meaning, and doing math. Teachers need to be sure to not have students just memorize the material. When we ask students to just memorize, we are not giving them a chance to actually understand why the procedure has one step before another or how we get from one fact to another. Instead, teachers should encourage students to think conceptually. By doing so, we are assisting students in developing different thinking processes. 

It is crucial for teachers to plan ahead when considering specific lessons in order to select a rich activity. There are three main parts, which include: selecting and setting up the task, supporting students exploration of the task, and sharing and discussing the activity. There are five questions teachers should ask when selecting and setting up the task:

1. In what ways does it build on prior knowledge, previous life experiences, and culture?
2.  What are all the ways the problem can be solved?
3.  What particular challenges might the activity present to struggling students, ELL students?
4.  What are your expectations for students as they work on and complete the problem?
5. How will you introduce students to the activity so as to provide access to all students while maintaining the cognitive demands of the task?

It is important for teachers to support students exploration of the task. We need to have questions ready to help them get starts and to stay focused and engaged throughout the activity.  The final part is sharing and discussing the task. This final step is so important because we need to make sure that all students are on the same page. The goal is to make sure all students comprehend the material, so sharing and discussing our ideas and work will benefit the entire class. 

From Smith, M. S. and Stein, M. K. (2012). Selecting and creating mathematical tasks: From research to practice. In Lappan, G., Smith, M. S. & Jones, E. (Eds.). (2012). Rich and engaging mathematical tasks Grades 5-9. Reston VA: The National Council of Mathematics Teachers, Inc.

Smith, M. S., Bill, V. & Hughes, E. K. (2012) Thinking through a lesson: Successfully implementing high-level tasks. In Lappan, G., Smith, M. S. & Jones, E. (Eds.). (2012). Rich and engaging mathematical tasks Grades 5-9. Reston VA: The National Council of Mathematics Teachers, Inc.

Groupworthy and Idea About Math

There are eight different math habits of mind. The habits include: exploring ideas, orient/organizing, thinking in reverse or being able to work backwards, generalizing, representing, justifying, math language, and checking for reasonableness. Our goal as teachers is to have our students acquire each of these math habits of mind and also making our students mathematically competent. We need to push our students to learn math more deeply. Teachers need to make math fun and engaging for students so they are excited to learn. It is important to have students interact with one another and work in groups during math instruction. In order to have an equitable classroom, we must establish norms for group interaction; for example, being respectful, taking turns, and listening to others' examples. 

Teachers also need to be sure that all students know there are multiple ways to contribute to math problem solving. This includes: posing interesting question, making astute connection, representing ideas clearly, developing logical explanations,working systematically, extending ideas

Like I stated earlier, it is important for students to engage in groupworthy tasks. When preparing for a lesson, teachers need to:

1. Focus on central mathematical concepts or ideas 
   
2. Involve some interpretation 
   
3. Provide multiple ways of being competent in problem solving
   
4. Perform in group bolsters students’ interdependence 
   
5. Require individual and group accountability 
   
6. Establish clear evaluation criteria
   
7. Present tasks laid out clear, simple directions, and has directions, diagrams, probing questions, and evaluation criteria

Although students are working with their groups, the teacher still plays a vital role. Before the lesson, teachers must think it through, consider challenges that may arise, and compile the various resources students may need. During the lesson, the teacher will need to walk around and check in on groups and ask spontaneous questions throughout. They must also make sure all groups remain on task. After the lesson, the class will need to come back together as a whole and discuss the task. It is also important for teachers to hold students accountable for their work. This can be done through group interaction or through formal assessments. 

From Horn, I. S. (2012). Strength in numbers: Collaborative learning in secondary mathematics. Reston VA: The National Council of Mathematics Teachers, Inc.