The Mobile Mathematician: Apps to Multiply Success
It is not new knowledge that math is clearly a hot topic in the 21st century. School boards have put forth great effort through professional development and curriculum resources to shift the direction and purpose of math education. When designing any lesson based on the curriculum, educators need to consider content knowledge building, thinking, communicating and applying knowledge. Over the past century, mathematics education has tended to focus heavily on content knowledge building through rote learning practice and the application of this knowledge through worksheets or standardized tests. Students have been exposed to math manipulatives for a long time now, but these learning tools have been used to support students’ success with standardized tests.
Of course, math content knowledge and application have their place in learning and are important for students to be successful. You can consider this type of knowledge as building blocks towards high order thinking. However, in the 21st century, the education system is seeing a dynamic shift from rote learning practices and tests to more emphasis being placed on recognizing, encouraging, valuing, and assessing students’ mathematical thinking and communication skills. With an importance placed on thinking and communicating, math in the 21st-century classroom looks a lot different. Educators are now encouraged to focus on students’ development of new knowledge in math. This knowledge is not necessarily new to everyone, but it is specifically a new understanding of math for the student that developed it.[Tweet “We should focus on student’s construction of knowledge instead of just the consumption of knowledge.”]
To support students’ construction of knowledge instead of just focusing on the consumption of knowledge, educators are now implementing more inquiry-based, project-based, and problem-based learning instructional methods. Problem-based learning seems to be one of the more prominent choices of collaborative mathematics instruction. Problem-based learning begins with teachers posing a question or problem that students then work in pairs or small groups to solve. The purpose of problem-based mathematics is for students to construct their own methods and strategies for solving problems, leading to the construction of new knowledge within the group. After students develop strategies to solve the problem, teachers usually hold a whole class congress where students share and compare their different strategies and discuss ways of potentially improving each other’s strategies. As you can probably see, mathematics education is more focused on a students’ process of learning rather than the product. Students’ are assessed throughout their math strategy development and further during their large group explanations. While this type of mathematics learning is progressing, the resources students are using need to fit the 21st-century learner. A previous blog post written for Learning Bird titled Teaching Students the Way They Want to Learn describes the unique skills and learning preferences outlined by Prensky (2001) with regards to students growing up with technology since birth. Students today respond and are motivated differently than their predecessors, and teachers need to consider this when developing their mathematics lessons. The current generations of students have developed skills to manipulate technology to support their learning. Today’s students are further motivated and prefer to learn through the interactivity and multi-modality within digital technologies.[Tweet “Today’s students are motivated by interactivity and multi-modality within digital technologies.”]
Research has also demonstrated the unique affordances of digital touch-based technologies like tablets to enhance 21st-century learning like problem-based learning. Apple iPads are specifically unique in their lightweight portability, their wide array of apps, their unique touch-screen interface, as well as their simplicity, intuitive design, speed, and affordability compared to other brands of tablets. With these features, tablets can enhance a blended learning approach by making learning accessible anytime, anywhere. Moreover, digital-touch based mobile technologies, like tablets, have the potential to support multimodality and students’ development of 21st-century literacies and skills.
With this context in mind, the following information provides an overview of mobile technology apps that enhance mathematics instruction in the 21st century. It is time to produce Mobile Mathematicians!
Apps for Problem-Based Learning
It is common practice for teachers to give out chart paper as a platform for students to work out problems and record their strategies. However, since most classrooms have 20-30 students and one teacher, it can be difficult to go around the room and record students’ thinking and communications. Important conversations between students are potentially missed, and the teacher does not always capture the full process of how students worked through problems collaboratively. It can also be difficult to capture how students are testing out different strategies and finally settling on a strategy to solve the math problem.
With mobile technologies like tablets, different apps have been developed to capture students’ thinking and communications. These apps are commonly referred to as screencasting apps. Screencasting apps resemble mini interactive whiteboards within the tablet. Students can use multiple modes within the screen-casting app such as drawing tools, picture uploading options, typing tools, and best of all, an audio recording tool. Now, this does not sound much better than what you could capture by just viewing students’ work on chart paper. However, with screencasting apps, these modes are captured throughout the process as students use them. Teachers can have students press the audio record option right away. As students’ conversations are recorded, their screen interactions are further captured at the same time. Students’ screen interactions and audio playback to teachers like a video as students’ progress towards their final product. With screencasting tools, teachers can playback the combined audio and video file to see students’ whole progression towards their final product. This can be extremely helpful when trying to assess students’ thinking and communicating.
Furthermore, since groups of students usually share their work in a whole class congress, the screencasting videos can be played back for other groups to watch. With this type of technology, students do not need to try and recount everything they did to form a math strategy and solve the problem. Rather, other students can see the whole process in action. For students who are shy, screencasting videos provide an additional opportunity for their voices to be heard without the intimidation of speaking in front of a large group.
Here are some examples of great screencasting apps:
Apps as Math Manipulatives
Hands-on learning is imperative throughout students’ learning process. However, in the digital era, hands-on learning does not always mean manipulating concrete objects. To this day, many educators use concrete manipulatives to demonstrate concepts and further have students practice these concepts. However, keeping in mind that students today have a natural and intuitive ability to manipulate and respond to technology, it seems more appropriate to have students practicing and working through problems with digitally enhanced manipulatives. Digital manipulatives provide students with the opportunity to still touch, slide, and tap in a hands-on manner. However, this process happens in a digital environment potentially better suited for digital natives.
With mobile technologies such as tablets, students can move more fluidly between screencasting apps and readily accessible math manipulatives while working to solve math problems. The portability of the tablet also enhances the use of these digital manipulatives. Students can easily rotate the tablet to show what they have done with manipulatives and can easily carry the tablet to the teacher or another peer to inquire and ask for feedback on what they have done. This process would be much more difficult with regular concrete manipulatives.
Here are some fantastic math manipulative apps:
Manipulatives have clearly gone digital! Furthermore, many math manipulative apps have built-in lessons to enhance self-directed learning through a blended learning model (i.e., Brainingcamp math apps). These apps can be used during problem-based learning activities to support students’ strategy development and problem-solving within groups.
Apps to Support Math Content Knowledge Building
It is imperative that educators do not eliminate the components of math content knowledge building. Students need to be equipped with a general knowledge and understanding of math content so that they have the tools to tackle different math problems. Math content knowledge building is a prerequisite for math knowledge construction. Tablet app developers have come up with a whole slew of rote learning apps to support students’ general math content knowledge. However, educators need to take a step back and not be too eager to download all of these different math apps. Educators need to look for certain features that will support a blended learning model for math education. Math apps for content knowledge building need to ensure self-directed learning through scaffolding and immediate feedback features. Furthermore, personalization features like the ability to set up separate student accounts enhance the teacher’s ability to modify math instruction for varying levels. Built-in reward systems will further encourage student motivation and self-directed learning.
Teachers need to ensure that the features mentioned above are built into math content knowledge building apps so that effective 21st-century instruction can happen. With more self-directed and personalized apps, educators can spend less time teaching content through traditional teacher-directed methods. Rather, teachers can spend more time encouraging student knowledge construction, strategy development, and problem-solving skills. In the junior, intermediate, and senior grades, content knowledge building apps can further be accessed and used at home so that even less teacher-directed instruction needs to happen in the classroom. Math content knowledge building apps can include games, instructional videos, or instructional videos with math manipulatives and interactive activities built in.
Here are some examples of math content knowledge building apps:
Prodigy app is an interactive math game that resembles Pokémon for primary, junior, and intermediate students. Prodigy learns students’ math skill level and provides appropriate math questions based on students’ personal math abilities. Prodigy also has personalized student accounts, built-in manipulatives for students to access when answering questions, reward systems, and immediate feedback to scaffold students’, correcting their answers and learning from their mistakes.
Check out this blog post on Prodigy: Are YOU Ready to Make Math Magical?
MyBlee is an interactive app for students to learn math content within instructional videos. The instructional videos, however, go beyond traditional video. Students learn through a gradual release of responsibility by watching demonstrations, practicing with digital math manipulatives, and applying knowledge through rote learning activities. MyBlee also provides immediate feedback to scaffold and correct student learning. It has multiple reward systems, personalized student accounts to support differentiated levels, and extra manipulatives for students to access when needed. Check out this blog post on MyBlee: Self-Directed Math with MyBlee
Math Planet is a math game app where primary and junior students can learn through different levels based on different math strand concepts. Each level is made up of fractions, number operations, geometry, and other number sense and numeration activities. As students work through the activities, they move on to different levels or ‘planets.’ This app has a great reward system and motivating features for students. However, there are some limited scaffold features and no readily accessible manipulatives for students to support learning.
Check out this blog post on Math Planet: 1, 2, 3…BLAST OFF to the Math Planet App by Playpower
Learning Bird Learning Bird is a mobile friendly web app offering a wide variety of instructional videos on all curriculum strands for students in grades 6 – 12. There is an abundance of math instructional videos that can be connected to the curriculum directly. Math videos on specific certain concepts can also be grouped into playlists for students to watch anytime, anywhere. Learning Bird provides each student with their own account, and the variety of videos that could be chosen for a playlist can support differentiated instruction. Furthermore, students who may be working at different math levels than other students can be assigned their own resources geared towards their math abilities.
Students need to understand the why and how of mathematics and its application to the real-world to become 21st century mathematicians. It is therefore imperative that 21st century math classrooms utilize tools that encourage students’ engagement in problem-based learning activities, scaffold student learning, and provide the math content knowledge needed to spark the construction of new knowledge. With mobile technologies like tablets, students will be equipped with the tools to build 21st century skills like critical thinking, collaboration, communication, computer and digital technology skills, and creativity. Essentially, students will become 21st century Mobile Mathematicians!