J/I Math ABQ: Math Manipulatives in the Classroom

Ugh, that moment you type up a storm and then BOOM! All gone in the blink of an electrical outage!

Bare with me as I try to attempt the rewrite of this ever so passionate discussion piece.

"Manipulatives are the equivalent to a real-life problem. Although the practical application of the skills being portrayed are different, there is an inherent relativity to the physical. As a logical thinker it should be an easy common understanding between Math and English educators that in order for students to understand a topic it is best when the pieces and variables are at hand, there in front of a person to work with the objects rather than a "hypothetical".

Take for example the candle in a four walled room problem. The classic psychological problem that seems to be less of a challenge as society steps away from candle usage and relies more on modern technology-nonetheless, this activity will be much more manageable when all the necessary resource piece are available to be used. When people have the parts to smash, mesh and manipulate the problem becomes tangible logically as well as mentally.

I once described to my students the importance of reading out loud. Students believe it is a weakness, however what is not recognized is that if a person never knowingly heard a particular word before, but are then asked to identify known words in a select reading, they will most likely not recognize it immediately unless reading it out loud. There are however students with louder inner voices and the ability to hear the word clearly in their mind. But for students who are still developing that inner voice manipulation, it is key that they read the word out loud in order to allow their eyes and ears to collect that data of those characters in that specific arrangement.

Similarly in a math problem, the more data inputs a person can create with the resources/variables, the more successful they will be in solving the problem. The reality of this phenomenon is that it eliminates some of the more benign questions that are not relative or necessarily important to the question-but may be important to the person solving the problem."

Another site worth checking out that might be interesting to turn into "manipulatives"

http://www.math4thenines.ca/resources.html

An Effective "UDL"?

This is a bit of a new title for a learning strategy in my opnion, a "UDL"? Hmmm. Well, from the way I understand this, there are things like scaffolding, "time management" and many of those other strategies we use so often as teachers.
Maybe in American schools there is a different name for them? A teacher made a video and posted to youtube, their "UDL's" in a couple lessons of Mathematics at the 8th grade level. Interesting is normally what I would say, expect the video didn't clearly introduce what was happening.
Nonetheless, for the course we are asked to discuss which of the "UDL's" we feel is most effective/important.

To be honest for a 7/8 class an exit ticket is most important I feel because a class will always be worried about social dynamics and depending on groups (as they are situated), there may be students who are pretending to listen and are good at tuning out/selective hearing. Exit tickets are private and a bit more personal so as long as the teacher has a good rapport with the students; it is extremely beneficial.

Taking a close look at a 3-Act Math Lesson

http://mrpiccmath.weebly.com/blog/coca-cola-slim

I could settle without the narrative-but meh.

This is a a relatively simple yet, empowering experiment for students that allows them to take a look at things in everyday life from a different perspective. This particular activity is done to represent the learning of Measurements (Surface area, volume, etc.) in Grade 9 students ON, Canada.

In regards to the big ideas that Marion Small introduces in her videos, I would like to believe that I am correct in saying that the BIG Ideas related to this problem are in the Measurement section 1. A measurement is a comparison of size in one object to that of another; 2. The same object can be described by using different measurements

.This lesson really speaks to the overall expectation (of grade 9 Mathematics Academic curriculum)  "solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures" (pg. 36) however, the specific expectations that we are looking at completing with this activity is "Solving problems involving perimeter, area, surface area, and volume." (pg.37). This is ultimately stating that, if a student is capable of restating the data of a problem and then solve the problem, they have completed their task. There is an expectation to which students are capable and aware of the mathematical formulas to help them solve and track their progress in solving a problem.

Teacher Talk: PLC Discussion on The Spiral of Inquiry

I was sitting listening to a presenter Dr. Gerber who was presenting to the staff at our school when I heard him mention "The Spiral of Inquiry", at first, thinking he made up some genius plan to introduce inquiry, I researched further and found-NO! Its a thing, in fact it is something that very much applies to students in most, if not all! This is great, this very much applies to what I am studying here in my Math AQ course! Check out the sources and information below from each source that I came across as I was reading. not a single wasted word space!

To answer my question of "what is inquiry based learning" (EXACTLY)-

http://www.noii.ca/spiral-of-inquiry/

The Spiral of Inquiry assists network schools in taking an inquiry-oriented, evidence-based approach to learning and teaching — one that focuses on making the education system more equitable through the provision of high quality learning opportunitiesfor all young people.

The Spiral of Inquiry has six key stages: scanning, focusing, developing a hunch, new professional learning, taking action and checking that a big enough difference has been made. At each stage in the spiral, three questions are asked: What is going on for our learners? How do we know? and Why does this matter?

The Spiral of Inquiry is about listening to learners and reflecting on our own practices as educators. The spiral image captures the nature of inquiry – a continuous process and not a fixed cycle. The six key stages in the framework help school teams take a disciplined approach to professional inquiry, but inevitably, the true process will be messy and you will move between the stages as needed. The spiral is never complete – new learning always brings about new questions, ways of knowing and new opportunities for our learners.

These two key resources will help your school get started and stay focused:

The Spirals of Inquiry: for equity and quality (2013) handbook offers specific inquiry tools, research evidence and examples from practice in BC schools. It presents an approachable and yet innovative framework for inquiry that is influencing schools and districts across BC and in other parts of the world. Proceeds from book sales go directly to inquiring schools. For information on how to order, click here.

The Spiral Playbook (2017) is a condensed, plain language version of Spirals of Inquiry and tells of the work of many educators in BC and the Yukon. It is also a fundraiser for the Aboriginal Enhancement Schools Network. You can obtain copies by contacting Jennifer at the BCPVPA offices. All proceeds go to educator leadership in developing Indigenous world views through small grants to schools.

How do we know what good times and ways to introduce inquiry based learning?-

https://elearningindustry.com/inquiry-based-learning-model

What is Inquiry-based Learning

The Inquiry-based Learning Model emerged in the 1960s, during the “discovery learning” movement and relies upon the idea that individuals are able to learn by investigating scenarios and problems, and through social experiences. Rather than having to memorize information from printed materials, instructors encouraged their students to conduct investigations that would satisfy their curiosity, help them broaden their knowledge base and develop their skills and mental frames.

It’s important to remember that inquiry-based learning is not a technique or practice per se, but a process that has the potential to increase the intellectual engagement and deep understanding of learners, urging them to:

• Develop their questioning, research and communication skills
• Collaborate outside the classroom
• Solve problems, create solutions, and tackle real-life questions and issues
• Participate in the creation and amelioration of ideas and knowledge

The 5 steps of inquiry-based learning

This is why inquiry-based learning includes the following steps:

1. Ask questions
2. Probe into various situations
3. Conduct analyses and provide descriptions
4. Communicate findings, verbally or in writing
5. Think about the information and knowledge obtained

The principles of inquiry-based learning

There are certain principles that govern inquiry-based learning and can be summarized as follows:

• Principle 1
  Learners are in the center of the entire process, while instructors, resources and technology are adequately organized to support them.
• Principle 2
  All learning activities revolve around information-processing skills.
• Principle 3
  Instructors facilitate the learning process, but also seek to learn more about their students and the process of inquiry-based learning.
• Principle 4
  Emphasis should be placed on evaluating the development of information-processing skills and conceptual understanding, and not on the actual content of the field.

The 4 forms of inquiry

There are four forms of inquiry that are commonly used in inquiry-based instruction:

• Confirmation inquiry
  Learners are given a question, as well as a method, to which the end result is already known. The goal is to confirm the results. This enables learners to reinforce already established ideas, and to practice their investigative skills.
• Structured inquiry
  Learners are given the question and the method of achieving the result, but the goal is to provide an explanation that is already supported by the evidence gathered during and through the investigative process.
• Guided inquiry
  Learners are only given a question. The main goal is to design the method of investigation and then test the question itself. This type of inquiry is not typically as structured as the previously mentioned forms.
• Open inquiry
  Learners must form their own questions, design investigative methods, and then carry out the inquiry itself. They must present their results at the end of the process.

In an instructional setting, inquiry-based learning can give instructors the opportunity to allow students to fully explore problems and scenarios, so that they can learn from not only the results, but also the process itself. They are encouraged to ask questions, explore their environments, and obtain evidence that support claims and results, and design a convincing argument regarding the way they reached to the end result.

Join us at the Instructional Design History Journey

A New Instructional Design Model Will Be Added Every Week! You are more than welcome to let us know if you would like us to cover an instructional design model and theory that is not included at Instructional Design Models and Theories. Simply leave a comment at Instructional Design Models and Theories.

What research is there about Inquiry?

http://www.educationalleaders.govt.nz/Pedagogy-and-assessment/Evidence-based-leadership/The-spiral-of-inquiry

The six parts of the spiral of inquiry:

• Scanning 
  What’s going on for learners? More emphasis is placed on teacher observations of students, in all circumstances. There are some difficult questions to ask, such as: Is it all right for some learners to experience challenging and engaging learning in one classroom while in the room next door the students are not? Scanning is not done overnight, can last two months, and may turn up surprises.
• Focusing 
  Where will concentrating our energies make the most difference? Focusing well will lead to informed actions, and usually means selecting no more than one or two areas so that the inquiry is "focused and deep". The authors point out that a common focus generates the momentum to transform schools.
• Developing a hunch 
  How are we contributing to the situation? "Hunch" is an important word – hunches may not be totally accurate, but it is essential to get them all on the table because they guide the focusing. Sometimes they might be well-established routines of the school or the classroom, and be relevant to your own school. Hunches need testing.
• New learning  
  How and where will we learn more about what we do? Teacher learning must be connected to identified learner needs. External expertise is important here and the school must make clear to externals what makes a difference to learners. We all need to know why new ways of doing things are better than what we did before.
• Taking action 
  What can we do differently to make enough of a difference? "Genuine inquiry needs space to take risks, make mistakes, and try again – and again". Changing things can also feel risky for some learners who then resist change, and in turn bring concerned parents. We need to build understanding for all, right from the outset.
• Checking  
  Have we made enough of a difference? Checking doesn’t have to be formal, or at a set time. It can go on throughout the spiral. The importance of trust should be a recurring theme throughout the cycle, and it certainly is true of checking.

3-Part Lesson Breakdown

I thought I would take a chance on explaining a 3 part class lesson before making one for my online AQ.

1. Before Lesson Activity takes place, "Minds On"

This is the step in which the teacher is posing the introduction to the purpose of the activity and priming students for the things they will be doing in the class and focusing on in the activity; see the list general list of things to do below:

a) Priming of "Prior Knowledge"
b) Introduction to the purpose of the lesson
c) Explain what the lesson will entail
d) Differentiation of instruction/activity if needed


2. During Lesson Activity, Taking place, "Working on it"

This is the part of the lesson in which students are working on the activity (together vs. independently), to solve a problem or explore a topic as much as needed to answer the call of the teacher posed at the beginning of the lesson. Teachers should carefully consider what exceptional students there are and how to accommodate their specific skill sets.

a) Differentiation
b) Knowledge Collaboration
c) Trial and Error Learning
d) Exploration of topic


3. After Activity, "Consolidation, Highlights, Summary"

This is the part of the lesson in which students are taking what they gained from the activity and collaboration while sharing ideas as a class. This is not meant to be the collaboration that leads to further exploration of topics; no, this is to allow students moments of self-actualization. Just like an essay, there should be no "new information" added to the activity, just conclusive thoughts from the activity as students and teachers understand.

a) Appraisal of knowledge/skills learned
b) Questioning of activity completed
c) Summarizing to group members (collaboration for consolidation)
d) Consolidation of things learned
e) Praise/Positive Reinforcement

Dr. Yong Zhao on "Learning in the 21st Century"

In a personal setting with the award winning educator and overqualified comedian, educators overseas were able to enjoy an entertaining and enlightened view on learning/education in the 21st century.

The seminar/presentation started at the access point of thinking in different cultures and the introduction to his family life. Along with belittling Ontario's Special Education Curriculum, Dr. Zhao was also talking about the closed minds people around the world carry with them into classrooms and life.

The introduction of what Dr. Zhao was talking about was aiming to inform as well as entertain educators, that the learning taking place is growing to accept exceptionalism from various sources in society.

Moving on through the roundabout way of explaining how to understand what makes students work, and coming  to the idea that the people who come out of education in the 21st century, need to self-actualize and determine what their potential is and find their use in society.

Honestly, for myself, he spoke of things that our school has recognized a long time ago-maybe some people needed to hear this again and maybe some people forgot. But in the end it was an interesting mix of comedy and a presentation of a professional "hot topic".

Later in the day, Dr. Zhao introduces the ideas of what can be successful in the class in regards to numbers, could also be detrimental to students.

Exhibit A) Vocabulary in English class, can one test every two weeks exponentially increase/improve vocabulary of students? Surely not, is there a short term grade influx that we could observe in some students? Potentially, yes. But overall, how can we improve long term benefits through assessment and evaluation?

Thought 1)   don't provide conclusive feedback/grade until students have completed the work that they need at the end of the actually learning goal, otherwise, why would they improve?

How does one support international teachers?

A survey came out from our school in which they basically wanted to know "How can we better support our International Staff?"

Thoughts? I had a few...

As a mentoring committee, its not all about drinking and partying-that may be nice; but sometimes its just about enjoying us time and offering people a different perspective; finding things that work or that they enjoy. To be honest, to be a mentoring committee is extremely difficult because the committee puts the onus of staff happiness on themselves.

How are you supposed to assist people when the problem might sometimes..be above you? For example, maybe new teachers are unaware how much work might be too much work in a week night-my first couple years at MLIS were basically work till 9pm/arrive at school 6am (alternating days) and then go home/class. I later realized that the amount of work we do here, never lessens; never changes in the way we want it to. Its always going to be one of those things in life that we feel like, "I can do more".

What think that the committee can do then is,

1) Positive vibes, build people up, offer kind words, supportive remarks, hilarious memes (not coworker targeted)
2) At Xiao Chi open with we have had another successful week, thank you for all that you do!If you need to talk to us, find us in our office. Winning money is great though-don't change that!
3) Have people share some cool hobbies and interests that have been done/practiced through the lives of teachers
4) Offering up positive motivations that keep people motivated throughout the day.
5) Recognize that we need to have a staff that mingles with people OUTSIDE of our staff! We are so hell bent on getting people to spend time together here, but then is there not that idea of circulation and mundane lifestyle building up? What I am trying to suggest is that we not just look at mingling with our own staff but reach out, obviously some people are too busy take the time to put themselves in surreal situations where they meet new people; or recognize that sometimes staff members want to get away from "coworkers" because when teachers meet teachers...they talk like teachers...You ever met the IBM folks? The American School teachers? The Medical School Students? Why not? If you have, when have you invited them to "staff events"?

 Please keep in mind the following things-
1) I love the committee and its members
2) this took a lot of critical and creative thinking., my initial feedback was going to be all bubbly positive and nonsensical stroking of how great things are for teachers involved; however-that is not how progress is made, even if you don't like or don't understand my ideas-I shared some things that might be useful.
3) Some teachers are young and just want a life in which they can try to meet people, we can tell them that "well that is up to you to do"; but in the end its up to the committee to think, "what are we offering; and to what extent do we offer?"

these are thoughts, take'em/hate'em-I shared, thanks for your time and good luck.