Module 9 – Positioning Students as Math Explorers with Technology – Part 1

Today, effective math teaching cannot be done without the use of technology in a classroom, especially in a secondary math lesson. The use of technology in a math instruction will make the process of learning more engaging as the National Council of Teachers states that: “An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking.” In other words, technology gives possibilities to enhance our math lesson. A high-quality math instruction I would expect to see the teacher provides with a laptop or computer, digital whiteboard as well as students, also teachers and students can have graphing calculators to help solving math problems easily and efficiently. In addition, I would guess teachers will use technology that can act on some math objects and react on mathematical things.

Technology brings learning math to life. Therefore, it is crucial to see in a math instruction some of the following tools to enhance and engage students in a more effective learning such that, Interactive media, Desmos, Codap, Flipgrid, Dynamics Statistics, Dynamics Geometrics systems, spreadsheets, videos, animations etc. Making math enjoyable and visual in a classroom goes beyond students’ engagement. It is also important to have students read math passages in a class to familiarize themselves with the jargon. Students can discover a lot of things in math with games, simulations, and digital tools. Math needs technology, class readings via textbook or classroom tablets and assignments with collaboration are two important tasks students need to accomplish to grasp the materials.

Technology in the classroom is critical. There are many 21st-century skills that technology provides many opportunities for students to practice. These skills include communication, computational thinking, collaboration, and critical and creative thinking. Project-based learning in the digital realm fosters the previously mentioned skills because students have learning experiences to practice those skills. I would expect to see teachers and students modeling how to solve problems and making their thinking visible using Chromebooks, iPads, and graphing calculators as they organize their thoughts on either those devices or on paper. I would listen to rich discussions where students use their organized ideas, supported by technology, to support their claims with sound reasoning. Furthermore, they would use their organized thoughts to counter each other’s claims or build on their peers’ ideas.

Technology in math classes empowers students to choose the most helpful tools to find solutions. Additionally, students can select how they want to show their learning and determine their learning pace. With technology, the teacher can truly be a facilitator of learning. They are not tethered to a one-size fits all model. The facilitator can set up a class where students may choose to learn from a menu of concepts. Technology allows teachers to replicate themselves by creating mini-lesson videos and modeling potential solutions to various mathematical concepts.

In a high-quality secondary math classroom where a teacher is using a technology-enhanced math task, I would first see students having full access to the technology.  In referring to access, I think about the ability to manipulate the technology, explore the technology and interact with others (peers and the teacher(s)) both verbally and visually in the use of technology.   I would expect to hear more than one way to approach the technology-enhanced math task.  Although the use of the technology may first start out scripted (cookbook-like), I would expect that as the task progressed, we would hear about and see different approaches and use of the technology.  I think back to the days of Geometer’s Sketchpad, when many of the activities started with scripted steps to follow but led to a really rich task that incorporated the new knowledge of the dynamic software.  This process enabled students to explore and question new concepts and ideas.  To further get at a high-quality technology-enhanced math task experience, the task should experience some limitations when trying to understand it without the technology.  This will help to emphasize what the technology does to inform ones understanding of the task.

Focusing on the hear part of the prompt:  students will be given opportunities to present their findings both orally and visually.  I would hope for an opportunity for students to give and get peer feedback on their work, not just from the teacher.

On the most basic level, students would have access to a variety of resources (the list is long both plugged and unplugged) to use in order to approach, attack, experience, understand and solve these math tasks.

I vision to see math classroom where both teacher and students have good working computer/laptop with all technology installed.  Learning environment is informal but purposeful and respectful. The purpose,  importance, pros and cons of Technology in Math is discussed.

Instructor is aware of the basic difficulty that students may encounter and give the explanation that includes why and how things should be done while encouraging students to ask questions. Students do not hesitate to ask lots of questions about Tech as well as math concepts and Instructor have appropriate answers connecting both .

Students had chance to work on a problem in group setting where students answer  and teach each other. Student learn when and how to use appropriate technology in order to answer math problems and having fun doing it.

In a math classroom where teachers are using technology-enhanced tasks, I would expect students to have access to devices (i.e. iPads, computers, Chromebooks,…) individually so that each students has the opportunity to utilize the device to explore. I would like to see students exploring and examining what would happen if…, Ideally students will be working in groups of 2 or 3 sharing their observations, and having discussions about the mathematics they are doing. I would expect the teacher to be walking from group to group commenting and posing questions to prompt students to articulate their thinking process, and to support them as they work on their task.

Depending on the task, technology should allow students the opportunity to explore and to communicate. Students will learn to question each other and justify their answers in a productive way. In order to make room for this kind of class, the teacher has to be intentional when creating or choosing tasks for students.

To be honest – the question really took me some time to work through – because the expectations (for teacher moves and students moves) seemed to be contingent on the context (or difference) in a secondary math classroom that culminates into a Regents Exam (if you are in NYS) or a class that does not culminate in a State exam. For example in a Geometry class that uses technology – I would expect to see students designing and creating (using geometric principals) – such as with Sketchpad – where they are creating or responding to a problem (such as recreating space invaders) – or even working with art infusion of geometric spaces (design), while the teacher is positing problems and then providing tools (serving as a guide to support or facilitate) not necessary lead, although there is room for mini-lessons. In a regents culminating class – I see the teacher having a larger role in mini-lessons around content specific to the curriculum (test) 0 but the student having choice in the types of technology to use to demonstrate mastery of the skills (or concept) introduced in the mini-lesson.