Category Archives: Uncategorized

posted on April 22, 2019

For K- 8 Colorado schools considering bringing in an education program in STEM, consider STEMpunk. Here is their program catalog: PROGRAMS HERE

It is not easy to find an extremely well researched and presented roll-in STEM experience.

One truly never knows where that spark of inspiration comes from engendering a passion for learning!

Engaging students in programs brought to schools enriches students’ experiences and interests.

posted on January 28, 2019

All institutions, by their very nature, contain a finite amount of knowledge representing the communal skills and learning of their employees. Well funded institutions who find skills or knowledge lacking hire more employees or outside consultants. Many K-12 entities lack the financial resources to exercise this option. That is why it is vitally important for local communities to participate in K-12 education either through on-campus interactions, or by offering opportunities in their own spaces.

Universities, with an abundance of professional educators, students, and meeting spaces, are perfectly positioned to offer enrichment to the K-12 community. Two examples that come to mind are the University of Colorado Boulder (CU) Wizards program: HERE and The Rockefeller University Science Saturday: HERE

Both offer incredible learning opportunities to young learners by carefully crafting how to present complicated topics to this audience.

The Boulder Center for Interactive Learning at Dawson (BCILD) hopes to learn about, and share, information on other such opportunities within K-12 communities.

Photos taken at CU Wizard event Boulder,CO, Saturday 01/26/2019

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 April 24, 2018

BCILD is embarking on collaborative projects to investigate both best practices and innovative ideas in the teaching of mathematics (K-12).

Firstly, we have developed a relationship with Italian high school mathematics teacher, and Global Teacher Prize finalist, Lorella Carimali. Lorella’s biography is listed below, as well as a translation of a recent presentation Lorella gave in Italy.

Secondly, we are collaborating on a math podcast project with the Dawson School in Lafayette, CO. Dawson middle school students are interviewing and producing podcasts with adults in the community on the topic of how they currently use math in their daily lives. This activity helps students understand and appreciate the importance of mathematics in the ‘real world’, and gives them skills in interviewing and producing podcasts. We will provide further details on this project as it unfolds.

BCILD is interested in investigating best practices in the teaching of mathematics and sharing these ideas with teachers internationally. We present Lorella Carimali here as an introduction to an ongoing learning dialogue with her about her teaching philosophy and teaching practice.

Lorella Carimali HERE

Lorella Carimali – Mathematics Presentation – 2017

To develop an all-inclusive classroom setting which encourages the understanding of mathematics in a holistic way, we need to take account of both the process of being involved with a mathematical problem from start to finish and develop a comprehensive understanding of the discipline. Becoming a competent mathematician involves not merely the memorization of facts, but entails a deeper development and enjoyment of confidently utilizing intuitive skills and creativity in the process of problem solving. ‘Creative enthusiasm’ must become part of the learning process in mathematics, and it can be used across other learning disciplines as well.

A community of learners engages high-achieving students in the process of teaching their colleagues. In this way, the high-achievers refine their own thought processes through improved articulation while the students who find the topic more challenging feel included in the learning process.

Student mistakes in approach or calculation are not seen as negatives in the inclusive classroom but are instead seen as opportunities to learn. Mistakes open doors rather than close them. Use mistakes to motivate students. No student should ever feel inferior because they make mistakes. Students should see the usefulness of mistakes in their process of academic growth.

The methodology used in the teaching of mathematics should be neither mechanical nor automatic. Teachers need to use creative materials and approach students in a way that reinforces the idea that student intelligence and ability is not fixed, but rather something malleable and changeable with practice, concentration, and support. Teachers need to put tools in the hands of students, and support those tools by providing the student with an awareness of their own cognitive processes and abilities. Success in this endeavor is achieved when everyone in the classroom is equally involved, leaving nobody behind.

Points to consider:

(1) Teach the process before you present the problem. Use imagination and creativity in your practice. Each individual has an area of personal growth. Potential does not always lead to actual output.

(2) The teacher should act as a change agent for the student, uncovering collaboratively the student’s personal cognitive processes. Autonomous thinking depends on understanding your own capacity and process.

(3) The teacher and student should always have the same mindset and be available for growth opportunities.

(4) Teachers need to work with students in understanding the entire process of mathematics from problem understanding, to working through the process of solving the problem, to being able to articulate their thinking and problem solving processes to others. High-achievers need to have the ability to explain how they process their understanding.

Integral to the learning success of every student is having their progress carefully and consistently monitored each and every day, thereby fostering continuous engagement between the student and the teacher.

In teacher planning and preparation, plan your approach around who you have in the classroom as learners. Leverage the skills and abilities of each student to both their own, and the group’s, benefit.

An interesting approach with students would be to create a theatrical play around mathematics learning because it is important to develop skills such as intuition, imagination, projecting, theorizing, deducing, controlling and evaluation to be able, in a second moment, to ordinate, quantify and measure sustainability of facts and phenomenon belonging to reality.

I experimented with this model in different contexts, applying it following the scientific method and I could verify that it works and that it is replicable.

Students could express their discomfort with mathematics in a theatrical fashion, and they could safely explore ways to explain concepts and understandings to their peers. Play creation is similar to mathematics in that concentration, considering each detail, curiosity, routine, and repetition are all involved. In plays, as in mathematics, you recognize your own limitations, and can view them as opportunities for growth.

Studying math means essentially to learn to think mathematically and to become conscious of one’s own reasoning method, mastering procedures and not simply applying them, and therefore being able to transfer to other contexts the mathematical skills assimilated. Another approach would be to create a game in which students create a company where they have to use mathematics in building a business and making appropriate decisions regarding marketing, management, and the financing of a business.

A student wrote: “she made me re-evaluate math by teaching me to see it not as a set of formulas but as a way to see life and be able to simplify it by reasoning”.

Confidence is competence. Confidence is built through each student knowing their own mental processing capacity. What did you do? How did you do it? Why did you do it? The sharing of these insights between students is vital to a student’s overall competency. The students develop into a team working together where mistakes are not ostracized, but instead act as learning opportunities. Sharing is a process that involves everyone, with all participants feeling included and having the ability to refine and define their own thinking. In this way, we can make a comparison between students and the individual players in an orchestra: they sound good playing on their own, but sound much better as a symphony.

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.


posted on October 17, 2017

Forward thinking K-12 institutions are already teaching students about collaboration, design thinking, coding, STEM, and experiential learning. There are, however, other skills that we should consider equipping students with for their multiple career, multi-cultural, and diverse futures. These skills include the ability to negotiate, and the capacity to resolve conflict. Contained within this learning is a capacity for empathetic understanding, logical reasoning, problem solving, articulate presentation of position, and the capacity to change your mind based on evidence or argument presented to you.

Being able to negotiate and resolve conflict necessitates the fairly advanced skills of being able to listen for, understand, and explain the point of view of someone else. If you develop this skill, you are more likely to be able to empathize with that viewpoint as well. In being able to listen to and understand the thinking of others, students should realize the importance of clearly and logically presenting their own point of view to achieve maximum impact with their peer group. A person must be able to listen for understanding, as well as convincingly present ideas so that they can be clearly understood and added to the discussion and deliberative process. If a child can develop these skills, it follows that they can become more competent negotiators and resolvers of conflict.

Almost everything we need or want in life is attained from some form of presentation to, and/or negotiation with, another person. Shouldn’t we equip our children early with these powerful tools?

At the Boulder Center for Interactive Learning at Dawson (BCILD), we are working with a professional in the field of negotiation and conflict resolution to bring these skills in any easily implementable form to lower elementary students. Facilitating the development of these skills in young learners gives them both an opportunity to learn valuable life skills, and an opportunity to practice and implement them in their daily interactions.

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:


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.