Category Archives: Elementary math

posted on May 4, 2020

intooba construction kits for K-6. The benefits of using physical kits for mathematics and engineering in elementary and middle school are:

  • students can learn the vital skills of collaboration, listening, and expressing/explaining their opinions;
  • students learn that they may need to attempt to solve problems multiple times in order to meet the requirements of the problem;
  • students use their hands and minds in construction thereby giving a visual and practical application to math and engineering;
  • teachers can “see” how children are thinking by observing how they construct their engineering/building challenges;
  • teachers can see how children are working together and expressing themselves in collaborative project work.

https://www.intooba.com/

posted on April 3, 2020

From my years of teaching elementary school, a few ideas come to mind on what are essential skills for young people to learn. They are presented here, in no particular order:

  • the ability to substantiate and articulate your thinking and viewpoint
  • the ability to negotiate and work within a group
  • the ability to take information from one place and use it in another
  • the ability and fortitude to try something and rework it to make it better
  • the ability to try something new
  • the capacity and interest to learn about the world
  • the interest in connecting in-school learning to the ‘real world’
  • the opportunity to be both teacher and learner

Finding few engaging manipulatives attached to curriculum to achieve these goals, I have co-developed several products for hands-on collaborative learning in a variety of settings: the classroom, in after-school activities, in homeschooling, and in summer camps. These products offer open-ended opportunities for students to experiment with curriculum supported ideas and creative-free-thinking. They offer the possibility for students to teach and learn from each other, taking time to listen and contribute while using visually stimulating hands-on materials.

The first, the intooba construction kit for K-6, (www.intooba.com) is designed for hands-on collaborative learning in STEM/STEAM engineering and math. Rods and connectors are used to solve over 25 engineering challenges, each with several levels of complexity. A math manual is provided to support common core concepts such as shapes, measurement, and estimation.

Our challenging engineering projects encourage collaborative learning in designing, constructing, and budgeting.

diskii math (http://www.diskii.com) is a hands-on math manipulative for grades 1-5. Our instructor manual offers ideas on learning such topics as algebra, logic, fractions, and decimals, and is based on common core standards. Students may learn both as teacher and student when working collaboratively with diskii tokens. Each token is associated with a unique name, color, and face offering three variables for problem creators.  Users can vary the complexity of the product by assigning an age-appropriate value to each token when creating challenges. We have developed both physical and downloadable token sets.

All of our materials require minimal instruction to set-up and use. No professional development is required for these easy-to-understand products which are supported by instructor and student manuals where appropriate.

posted on November 26, 2018

I was always concerned in my elementary classrooms when I realized that my students principally saw only finished product in their lives – film, novel, technology, building, business. When are young students these days ever exposed to process other than through concerted efforts on the part of educators to show, for example, how stories are deliberately constructed? Children meeting professional authors offers an essential insight into how ideas are formed, massaged, written down, and ultimately formed into a story through diligent effort and many re-writes. Such is another limited example of students seeing process. In previous times, children were directly involved in family businesses or farming where they were personally involved in the process of production. How does something start, and how do people get it to completion? Not knowing how to connect a topic of study to its practical outcome in the ‘real world’ could lead students to question its relevance to them.

Some of the steps involved in what I will call “the creation of something” are:

– the idea itself
– is it a good idea or not? What are its benefits to me or others?
– is the idea an adaptation? I need to draw information from various sources
– working the idea to a place where it can be explained to others
– seeing if the idea already exists, and if/how this impacts our moving forward
– ascertaining what we need to complete the project
– getting others to cooperate in the execution of the project
– assembling the resources to complete the project
– trying and failing
– trying again and failing
– not getting despondent and keeping resources focused on the project
– trying again, and hopefully succeeding

These are but a few steps in general idea and project conception, process, and completion.

In elementary mathematics, providing opportunities for students to use their hands and minds in a cooperative learning environment are somewhat limited. To that end, we have invented two products for elementary education which help children work physically towards solutions either individually, or in groups.

Aspects of our manipulative products are discussed below:

intooba – intooba HERE

This K-6 construction manipulative offers many lessons in both specific mathematical concepts such as shapes, estimation, and fractions and in engineering challenges. In math, we provide a spiraled program offering teachers instructional ideas in many math concepts. In engineering, we offer students over 25 construction challenges each with varying levels of complexity.
This is hands-on work asking for actionable solutions through construction and mathematics. Resource constraints such as assigning a project budget and input costs makes this learning very relevant.

diskii – diskii HERE

This K-4 manipulative offers students and teachers opportunities to explore mathematical concepts hands-on either individually or in groups. Our ten tokens (essentially representing 0-9) have unique names, faces, and colors offering many layers of complexity in problem construction. Instructional possibilities include logical reasoning, understanding the equals sign, and substituting a token for an unknown algebraic quantity x as in: token + 4 = 10 for lower grades.

Drawing on information to solve a problem is a critical skill. Using diskii, equations can be created where certain token values are given, and students have to use this information to solve for the unknown tokens.

We have created these advanced thinking manipulatives with lesson support to offer easy-to-implement hands-on group problem solving opportunities we feel are unavailable in many physical manipulatives available in classrooms today. We focus on fun, creative visual challenges making math relevant in concrete ways to elementary learners.

In our manipulatives, we are diligently focusing on process as an integrally important part of learning. Students work cooperatively with their hands and minds to solve challenges.
In this environment, drawing on spiraled learning, students have opportunities to produce increasingly complex product through their own efforts.

posted on July 2, 2018

Spiraling through the many years of a K-12 education are various levels of math, language, writing, social studies, the sciences, and the traditional topics we expect in such an environment. The education community is pushing towards STEM/STEAM (Science, Technology, Engineering, Math – with the inclusion of Art) with the realization that the space in which students will eventually be employed has changed dramatically. Not only has the environment changed with advances in technology, globalization, access to information, social and political change, and environmental challenges, but the pace of change is increasing. We are now trying to integrate the disciplines with a view to increased creativity through cross-discipline pollination. Is this enough? Are we fulfilling our essential and critical responsibility in providing opportunities to enable our children to operate successfully in this environment?

Essential features in education looking forward should include:

• learning to correctly and accurately find, describe, and solve complex challenges
• attaining the skills required to work successfully in groups
• the ability to welcome and work through adjustments, modifications, and failures
• demonstrating to students the practical applications of their classroom learning

To these ends, we at Blue Egg Advisory Group LLC have invented and developed a unique manipulative to foster these concepts in young learners (K-6) as they prepare for secondary school and beyond. Our INTOOBA Construction Kit manipulative offers many opportunities for hands-on experimentation through leveled curriculum manuals in math and engineering.

http://intooba.com

posted on April 13, 2017

As we aim to teach students how to solve complex problems through critical thinking and design thinking, we enable them to think as individuals but work collaboratively. This profound skill set truly enhances capacity to reason logically within the framework of an ability to comprehensively understand the challenge.

Our capacity as educators to see thinking is often challenging. One solution is to afford students an opportunity to work with physical manipulatives:
HERE

posted on September 1, 2016

In integrating collaborative work in our approach to K-12 education, we are teaching students the benefit of listening, learning from others, coming to consensus on ideas, and other group dynamics. These are all essential skills in group problem solving exercises in school, and in adult project based work. What we should not lose sight of is both valuing the individual as a contributor, and building personal communication skills thereby promoting effective group dialogue and collaboration. It takes a very skilled teacher to nurture the individual as a person of abilities, aptitudes, and evolving capacity while at the same time teaching effective group dynamics. Productive group work is predicated upon individual skills in communication, and group skills in collaboration. We want children to know that their opinions and observations are highly valued, we want them to have the skills to communicate them effectively, and we develop collaborative skills to make project based learning effective.

In early development of these skills, it may well be the case that using physical manipulatives in the classroom facilitates the development of communication skills across curriculum topics. As personal skills in, for example, vocabulary, persuasion, reasoning, and advanced thinking develop, children could use manipulatives to assist them in communicating their ideas with peers. This is evidenced in the example of Kim Haines, 4th grade teacher at Dawson School in Lafayette, CO who used the INTOOBA Construction Kit in developing communication skills in listening, giving directions, providing clarification, and in either being a giver or receiver of information in her math class:

Blog HERE

Essentially, teachers can observe individual thinking and development of these essential skills through the use of manipulatives while also noting the child’s functioning within a collaborative setting. Children here are supported in the learning of specific collaborative language through the use of their hands.