How was Math Out of the Box designed?

Math Out of the Box is a K-5 mathematics curriculum which is under development in the College of Engineering and Science at Clemson University and is published by Carolina Biological Supply Company, Inc. The development team for Math Out of the Box is made up of educators with a rich diversity of experience. They are teachers from all levels of education. They have been leaders in professional development as well as math reform. Each lesson has been tested in the classroom numerous times under the supervision of the principle design team. It is not uncommon for first time users of Math Out of the Box to compliment us with the statement, “This looks like it was written by teachers!” More . . .

How is Math Out of the Box different from other inquiry-based math programs?

Math Out of the Box distinguishes itself from other inquiry-base math programs in the areas of differentiated instruction, professional development, curriculum design, transferability, material support, and community support. More . . .

What is the Learning Cycle?

Math Out of the Box uses a learning cycle to foster inquiry-based learning. The learning cycle used in the lessons gives teachers the structure that is needed to reach their students, whether they are traditional or inquiry-based in practice. The learning cycle provides teachers with a template that promotes the development of active inquiry and critical thinking. The learning cycle allows students to make connections between past and present learning experiences and is based in the “cognitive principle of assimilation,” which implies that understanding cannot be imposed on the learner, but instead is developed progressively by the learner, beginning with concrete and progressing to abstract opportunities. The learning cycle provides the opportunity for students to share ideas with others and to more formerly connect what they have learned with what they already know. More . . .

Why is communication in the classroom so important to this program?

Discussion, questioning, reflection, and writing are communication strategies that ensure that meaningful mathematical thinking occurs in the classroom. The communication model used in the lessons provides opportunities for verbal and written communication from pre-assessment brainstorming at the beginning of a lesson to individual accountability at the end. It provides a structure in which students learn to successfully communicate mathematical ideas both verbally and in writing. Communication permits learning to build on the students’ informal knowledge, gives students practice in explaining their mathematical thinking to others, and provides students and teachers with evidence that learning has occurred.

The communication model builds a community in which students have the freedom to take risks so that verbal and written communication can occur and develop. In the lessons, communication evolves and improves as discussion and writing moves from part of a community to individual accountability.

The communication model ensures formative assessment is taking place. Based on this model, teachers learn to assess on a regular basis while the lesson is being taught, not just at the end of a lesson or unit.

Why is the reflection an important part of the Math Out of the Box program?

The communication model employed in the lessons is based on research that considers the reflection to be essential to the learning process. Two types of reflection occur in the lessons—reflection-in-action, which is known as “thinking on our feet,” and reflection-on-action, which involves exploring why we think the way we do. The learning cycle provides a structure for continuous reflection-in-action as students represent, verbally communicate, and compare their findings throughout each lesson. The Reflect phase of the learning cycle provides an opportunity for focused reflection-on-action as students are asked to examine and explain their thinking by writing about what and how they have learned. It is through this linked process of reflection, in-action and on-action, that students take responsibility for and ownership of their learning.

Teachers have an opportunity to reflect after a lesson to be aware of the teaching strategies they are using, what changes are taking place, and how students are learning and interacting with each other. There is also a reflection process built into the Professional Development so teachers have an opportunity to hear reflections from others.

In order to meet the requirements of our district, we are struggling to fit in everything in one day. How can we teach Math Out of the Box and still fit in everything else?

Different schools have different amounts of time scheduled for mathematics instruction. The Math Out of the Box lessons are designed to be flexible so that teachers can break a lesson between any phase of the learning cycle. The lessons are also designed to connect with other curriculum areas. Data collection in science, analysis of graphs and charts in social studies, written reflections in writing, and connections to literature all enrich mathematics lessons throughout the school day. Ideas for art, music, and physical education connections are included in the lessons. Whenever connections can be made between curriculum areas, efficient use of time is ensured.

There are many questions provided in the Math Out of the Box program that help teachers facilitate learning in the classroom, but there are no answers to these questions. How can we make sure students understand the material without the answers?

All learners, including teachers and students, offer varied perspectives based on prior experiences and opportunities. Specific answers to the questions are not provided in the materials for two reasons, both learned during field testing. During the first round of field testing, answers to the questions were provided. Two different phenomena were observed. In several cases, teachers actually taught the answers, prior to asking the questions, which is not how the questions are intended to be used. In other cases, teachers would ask the questions, without providing the answers, but if answers were given that were different from those provided in the materials, these answers were automatically rejected as wrong, when in fact they were acceptable answers. In the next round of field test, the answers were omitted. In this case a new phenomenon occurred. The questions provided a rich source of discussion for teachers and teacher leaders. Discussing possible answers to the questions with peers and instructional leaders prior to teaching the lessons became commonplace and actually provided an imbedded source of professional development that occurred naturally in the teacher’s daily planning routine. By discussing these questions among peers and with instructional leaders, the teachers developed deeper understandings of the concepts they were teaching.

We are struggling to find enough grades for our students. How can we use the lessons in Math Out of the Box to acquire more grades for report cards?

Adjusting to an inquiry-based curriculum takes time. When beginning Math Out of the Box, teachers are dealing with issues such as materials management, collaborative grouping, and classroom discourse. Becoming used to formative and summative assessment instead of focusing on evaluation of every piece of student work requires a paradigm shift. After teachers become experienced with Math Out of the Box lessons, they learn to make genuine assessments of student learning. Teachers new to Math Out of the Box can use the checklists matched to each subconcept to track student learning, give a traditional grade to individual student work, and grade the post assessments in a traditional way.

How can teachers being exposed to Math Out of the Box for the first time be expected to launch the program successfully into their classroom with only two sessions of Professional Development?

The two days of formal in-service are designed to provide a vertical overview of the mathematical ideas from the curriculum strand, to introduce the instructional materials to teachers, and to provide teachers with inquiry-based experiences as learners. Beyond the external formal professional development, the curriculum materials are designed to provide learning opportunities for teachers that occur within the daily routines of the teacher. The higher order questions that are presented throughout each lesson provide rich sources of mathematical and pedagogical discussions for teachers and teacher leaders, which can be used during planning and/or lesson reflection sessions. These same questions, when asked of children with varied prior experiences, offer teachers and students opportunities to learn and think about the mathematical ideas in many different ways. The learning cycle lesson design provides a framework for inquiry-based instruction in which the teacher learns throughout the implementation process. This imbedded professional development make this program unique in that teacher learning occurs not only in external formal events, but also throughout the implementation process.

How do we use the literature connections list provided in the teachers manual if we do not have any of the books in our library?

In preparation.

In this age of accountability, how does the Math Out of the Box program prepare students for annual testing?

In preparation.

My students are seeing connections that I didn’t identify, and honestly, sometimes make no sense to me! How can I prepare myself to deal with this phenomenon?

Students and teachers bring varied prior experiences to the classroom. Learning that students have rich and accurate mathematical ideas you did not “teach” to them is often a surprise! Recognizing that this diversity in thinking actually contributes to the learning of all participants, students and teachers, is an important benchmark on the continuum of becoming an inquiry-based practitioner. The best preparation is to learn to be open to unexpected ideas and to learn to say “I don’t know about that. Let’s think about it some more.” Then run across the hall and ask for a second opinion!