HOPE Reflection H2 – Honor Access to Content

H2 – Honor student access to content material. Teacher candidates use multiple instructional strategies, including the principles of second language acquisition, to address student academic language ability levels and cultural and linguistic backgrounds. Many regard mathematics as a second language. Mathematica notation and use of mathematical vocabulary areLessonPlan LessonPlan 1essential to learning this topic. At the school where I work, all students are fluent english language speakers, it is unusual to encounter a language barrier in communication. Most of the language acquisition problems are through the understanding of mathematical language. To address this HOPE standard, math teachers must make the mathematical language more accessible by planning in vocabulary acquisition and teaching concepts and then naming the concepts.

The evidence I am presenting is two photocopies of some lesson plans where I am introducing two new topics. The first I am introducing students to sequences and series. In this lesson, students start with the Entry Task (ET) and are asked to complete “the list of numbers”. Since these are the teacher’s notes, the ideas are just brief notes. After the entry task, the plan is to formally put a name to “a list of numbers” which we will call a sequence. Similarly, as the lesson continues, I plan on clearly indicating and showing students the notation and the vocabulary for the notation about how to write a sequence. When I introduce combinations and permutations on the second lesson plan, I first mention “what are the possibilities of rolling two dice?” This removes technical language, the words “combination” and “permutation” and “the basic multiplication principle” are not even mentioned until the next day in class when students have acquired the conceptual understanding.

By removing the barrier of technical language students feel more comfortable with the content. The teacher will avoid the use of confusing language, but if a student uses improper language (such as the note about the difference between probability and odds in the lesson plan), the teacher will address the students misuse of language and avoid confusion of the vocabulary in the future. The HOPE standard is met because the teacher is planning for proper language acquisition and preparing students to understand content and then later naming that content when students struggle for a word to name the idea.

Over the course of my teaching internship, I have build knowledge and understanding of how to introduce new ideas to students without complicating the matter. From creating lessons that revolve around language acquisition and notation, I have learned that while I may have a deeper, technical understanding of mathematics, many students do not, and become intimidated by advanced language. By using lower level language, many of my challenged students become engaged.

Since many students are apprehensive about mathematics, this technique for introducing new ideas is helpful for students who are overwhelmed by math language and concepts. Providing instruction in an order that is helpful not to overwhelm students is important, especially in mathematics where there is a risk for pushing students away from the topic. To improve my understanding of this program standard, I will need to interact and prepare planning for more students who have different language needs, especially english language learners or those who lack significant mathematical skills. Since this HOPE standard is similar to Differentiation, I hope to address language acquisition, use of language and assisting english language learners as an improvement to my practices in differentiation.


P1 – Intentional Inquiry and Planning

P1 – Practice intentional inquiry and planning for instruction. This means that classroom teacher plans instruction around a learning target and creates a lesson which encourages students to critically think about the function of the learning target. Within the realm of mathematics, students should build intuition around how mathematical processes and can therefore build from current understandings to unique situations in the future. For a teacher, building this intuition must be well planned.

Student Work Matrix POGILStudent Work Matrix POGIL2Student Work Matrix POGIL3 Student Work Matrix POGIL4

Student Work Matrix POGIL5Student Work Matrix POGIL6

In the images, I’m presenting the work of a group of students who completed a group inquiry activity that was monitored me. While POGIL (Process Oriented Guided Inquiry Learning) activities are highly structured and I lack the training to adequately design a true POGIL, this is my best attempt at guiding students through mathematical concepts using discovery as the motivator for the lesson. This POGIL is about matrix multiplication, the purpose of this activity was to build on their prior experiences of matrices, create intuition about mathematical practices, and assist students in making meaning behind matrix multiplication. Many students know the procedure, yet few understood how this process was applicable in the real world.

This classroom activity was built and designed by me, although I used a textbook to find problems with student interest in mind and adapted the questions to fit my instructional goals. Since this activity was designed by me, this demonstrates I am able to ask students good questions which lead to conceptual understanding. This also shows my ability to plan for 100 minutes of instruction and facilitate an activity, probing students for more advanced thinking.

While planning this activity, I learned about how challenging it is to create clear questions which lead students to understanding of the learning targets. Since I teach multiple sections of the same course, after each class, I revised my questions to ensure each question challenges students and leads them to more complete understanding of matrix multiplication. Students also state they enjoy the POGIL’s as a learning activity. Students get to work in groups and ask questions to their peers. Providing group based activities, students break the routine of back to back 100 minute learning segments. Additionally, this provides students the opportunity to practice new skills without the traditional “drill and kill” of many math classroom. Practicing with inquiry also helps students create meaningful understanding rather than the process of symbol manipulation alone.

When designing lessons, it may be useful within my lesson plans to prepare questions each day which probe at the students understanding. Also, I think that creating a classroom goal everyday (and actively writing it down in the lesson plan) will help lead to a meaningful result from the lesson. With a goal like “Students can understand the meaning and operations of matrix multiplication,” I can create quality lessons, ask questions which probe for understanding, and measure the effectiveness of my lesson.