Category Archives: Teaching materials

Recommended additional sources for enriching the curriculum

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 August 10, 2019

As elementary school teachers, we developed an entrepreneurial after-school program for grades 3-5.

We felt that it was important for younger students to develop a solid understanding of business and the economy. Our program consisted of three components:
(a) visiting local businesses, noting physical positioning, product, and range of service;
(b) playing a virtual stock market game: GAME HERE;and
(c) creating a product from concept to design to packaging and marketing.

I have not seen many programs on this topic. Recently, however, I met an elementary educator who has developed an extensive curriculum in business development ideas for elementary and middle school students. Eva Foxwell’s materials include curriculum material on entrepreneurship, business skills, and career development: CLICK HERE

We do not know where students’ interests and passions will lead them later in life, but it is certainly advantageous to offer early insight in careers, entrepreneurship, business, and economics.

posted on December 17, 2018

Through the use of classroom manipulatives, we can encourage a wide range of thinking and questioning at the elementary level. Using sets of diskii where each of ten tokens has a unique name, face, and color, we can avail students of opportunities to work collaboratively to solve hands-on problems. The opportunity exists to vary the complexity of the challenge according to the topic or grade being taught.

In a very simple example, consider the equation 3+4=7. We could ask students what 3+4 equals. There is one finite answer. However, using diskii we can ask what the possible values of the tokens are if: token + token = 7. Already, the complexity of the challenge is increased. Alternatively, we could set the value of one token at 3, and ask what the value of the remaining token is if: token + token = 7 given that one token has a value of 3. Here, students have to retrieve information and apply that knowledge (two critical learning skills) to solving the problem.

diskii HERE

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 March 22, 2018

Logical thinking, the process of moving sequentially from one thought to another in order to reach a conclusion or solve a problem, is an essential skill. Teaching this complicated process to young students can be challenging. However, using the INTOOBA Construction Kit, students can construct physical models and see an explanation of how logical thinking works.

Exercise: teacher assigns values to the rods and connectors. Students are asked to logically establish what is missing in the figure and what they need to complete the construction. They are asked to give values to what they see, what is missing, and what a completed piece would be worth. Students are asked to complete the model, and share their thinking process with the group.

Students use logic to establish what is missing, and then use their hands to solve the challenge.

INTOOBA HERE

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.