As an educator, I strive to deepen students’ understanding and connection with the modern world through innovative approaches. The foundation of their learning begins in the classroom. It is my responsibility to facilitate their learning, by enriching students’ lives with hands-on activities and experiments using technology while making connections across disciplines and to the real world.
What I see as invaluable is the mathematical discourse that takes place in the classroom among students. Whether it be through warm-up, number talk, exploring our investigations, whole group, small group discussions, summarization, or journaling, students take ownership of their learning and use Accountable Talk Moves to discuss their understanding of mathematics. I want to build on that foundation and strengthen students’ mathematical discourse by digging deeper into the meaning of the vocabulary in mathematics by incorporating the “flipped classroom” and vocabulary digital journaling. Not just simply following and memorizing steps in solving an equation.
Helping students develop meaning of mathematical vocabulary and using the vocabulary to make connections in the real world is crucial in understanding the purpose of mathematics as a disciple, not a subject matter. The question that needs to be answered- “Why?” Why does math “work” the way it does? Before students can use mathematical concepts, skills, and strategies, they need to have a deep understanding of the reasoning or proofs that hold rules and formulas true. They need to understand the meaning of the vocabulary and its applications in order to increase and improve their mathematical discourse in the classroom. This will help students find meaning beyond the classroom and apply the mathematical discipline in their personal lives and as they explore the world around them.
As students explore the mathematical investigations, which are richly student-centered and hands-on, connections will be made with the vocabulary and its applications. To foster their understanding they will create a vocabulary digital journal to showcase their deep understanding of mathematics as a discipline. As they become fluent with the discipline, they deepen their understanding, they will make connections, and be able to solve problems in the real world.
Students will increase and improve mathematical discourse in the classroom by developing meaning of the vocabulary and make connections to the vocabulary in the real world. Students will find meaning in math beyond mathematical vocabulary they are exposed to in school, and they will use these terms in their personal lives and to look at the world with a math perspective.
Determine Acceptable Evidence (Performances of Understanding)
Throughout the year, there will be ongoing performances of understanding to show that students have a deep understanding of the vocabulary as they improve mathematical discourse and make connections to the vocabulary in the real world. Theses performances of understanding will be formative (formal and informal) and summative assessments that will showcase students’ understanding by working collaboratively and creating mathematical meaning.
Learning new terminology is not going to happen overnight in any grade, let alone 8th grade, so, after I assign students a flipped lesson on prerequisite terminology they should have acquired in previous years, I will hold them accountable by a written homework task to take notes, write the definitions, and draw a picture associated with the vocabulary term. This will prepare students, refresh their memories, and be ready to explore new ideas in math for each unit this year.
As we work on warm-ups, number talks, investigations, whole group, small group discussions, and summarizations, a point system will be used to hold students accountable for using Talk Moves during discussion. This will help foster mathematical discourse. Every day, a different students has the responsibility to document participation points for whole group discussions. Bonus points will be earned for using the new vocabulary acquired through the explorations of new mathematical concepts learned. As they explore, they will uncover the “why” math works the way it does and why we need it. As I assess students’ journals, a rubric will be used focussing on mathematical language, understanding, and application by students given their own examples of the discipline learned.
To motivate students to remain on task during small group explorations of the investigations, I will use ClassDojo to reward groups with points when they are on task, collaborating, coaching one another, using appropriate talking levels, and using the Talk Moves as they discuss.
Throughout each unit, students will apply their understanding of the vocabulary to create foldables (interactive notebooks), create and solve real world problems, and create their own digital vocabulary where they will work in small groups to create a rap, meme, gif, or video story problem to showcase their understanding of the vocabulary and connect it to the real world.
Plan Learning Experience and Instruction
Context: I am entering my fourth year at Nobel Elementary School as the 8th grade math teacher. In the past, I have had about 78 8th graders for math, but this year there are 100 students divided into three 8th grade classrooms. The diverse learners will be divided between two classrooms, mine and the language arts teacher, and the third classroom will have the bilingual pull-out students which will be the science/social science teacher’s homeroom. The student population at Nobel is about 85% Hispanic, 13% Black, and 2% Other; with about 95% low income, 14% diverse learners, and 34% Limited English.
My classroom is set up in groups, with 6 groups of 4 students and 2 groups of 5 students. I create groups based on the population of the classroom. I have heterogeneous groupings which include algebra students, regular education, diverse learners, and bilingual students. I also make accommodations with seating that best meets the needs of the students. I have two tables in the classroom to pull for small group instruction or intervention.
I have a write board at the front of the classroom, document camera, MacBook, and for the past two years have worked with a SmartBoard. Students go to the computer lab every six days during preparatory periods and we use MacBooks in the classroom every six days, as well. I have extra space in the classroom and house 7 Dell computers for student use. When appropriate, students may use calculators and manipulatives are readily available for the exploratory lessons.
Classroom Norms and Talk Moves are displayed and used in discussion. I have a bilingual word wall that I update with each unit and refer to when translating words from English to Spanish for my non-English speaking students. I also have a data wall where only NWEA scores are charted to see the trend and growth for each of the three classrooms. My classroom also has a library for students to check out books for their reading pleasure.
Content: I want students to increase and improve mathematical discourse in the classroom through helping developing meaning of the vocabulary and make connections to the vocabulary in the real world. I seek answers to the following questions: How can students find meaning in math beyond mathematical vocabulary they are exposed to in school? How will they use these terms in their personal lives or to look at the world with a math perspective?
There are a few challenges on the way to achieving this big idea. For one, students may not have the technology at home to view the flipped classroom prerequisite vocabulary lessons. I will take a survey at the beginning of the year to assess access and offer a solution. Another challenge will be to translate the flipped lessons into Spanish.
Pedagogy: At Nobel, we follow the Math Workshop Model. I see all three 8th grade classes daily for 90 minutes. At the beginning of each class, students enter the room and begin their warm-up. These are problems that students are familiar with from previous lessons. If students are stuck, they may ask a person from their group to coach them.
After the warm-up, we do a Number Talk where a problem is presented to be solved mentally and related to the topic within the discipline. The students are divided into three groups and have a different number talks to solve from the other two groups. The following day, the number talk gets rotated and so on. I use this strategy to get more participation with mathematical discourse among the students. Students tend to participate more in these group settings, because more ideas and solutions are shared within the smaller groups as opposed to having 3-4 students respond to a number talk out of 33 students. More opportunities for students to participate.
Before we begin a unit, students will be assigned a flipped lesson on mathematical vocabulary that students should be familiar with. This will save class time. Instead of reviewing these prerequisite concepts in class, they will already have it reviewed, so we can begin with the Launch and Explore of the Investigations in the CMP3 resource.
The Explore is student-centered where the students work in groups to explore the topic within the discipline. Students use manipulatives, graphs, tables, etc, to show their understanding of the concepts. Throughout the Investigations, students will also create foldables (interactive notebook), memes, gifs, raps, and/or stories while utilizing the vocabulary and creating real work problems of their own.
The summarization will come after the students had time to explore and uncover the “why” behind the mathematics. Students know what they are going to learn through objectives, but now they will understand why. After the summarization comes the journaling, where students reflect what they have uncovered.
Technology: There are many technologies that I will use throughout the year. The flipped classroom is big and I am eager to learn how to create my flips, implement them, and get the students just as excited as I am. The time that will be saved in the classroom to uncover misconception is very important.
I will continue to use the SmartBoard to display the warm-up, number talk, Launch investigations, show educational videos, and share the students’ digital vocabulary journals, memes, gift, and stories.
Students will continue to use manipulative and hands-on learning with their explorations and foldables to foster their learning and facilitate the connections to the real world. All of these components will increase and improve mathematical discourse in the classroom through helping students develop meaning of the vocabulary and make connections to the vocabulary in the real world.
How can students find meaning in math beyond mathematical vocabulary they are exposed to in school? How will they use these terms in their personal lives or to look at the world with a math perspective? My questions will be answered...
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