Math Inquiry

In my group, the Weavers, I have committed to trying inquiry in Math.  In the last month, I have been very close to giving up that goal.  I was really not sure how I could possibly integrate inquiry into math.  There are too many foundational skills that have to be mastered before students can move forward.  This work is far too important for me to give up as much control as inquiry requires me to.  Then I had a conversation with a math teacher in the district who is finding success with presenting her students with one cognitively challenging task and allowing them time to explore the problem with an understanding that students will not necessarily complete the task with success.  Her focus is on the process that they go through as they collaborate in an attempt to find a solution to the task.
Talking to her made me realize that I don't have to approach inquiry in math as I might in science.  Math inquiry can be truly 'mini,' focusing on a very small objective that I want the students to master.  I decided to give it a shot.


My students have been learning about fractions.  They have been composing and decomposing fractions, learning about equivalence, and learning about the reasons why we add and subtract them the way we do.  I decided to try allowing my students the opportunity to "discover" how to multiply a fraction and a whole number.

We started by activating our schema around how we multiply.  Collectively, we found four strategies for multiplying: by writing out our understanding that multiplication is x, counted y times (skip counting), creating equal groups, using arrays and by adding repeatedly.  Once we made that list, I shared the objective with students: They will learn how to multiply a whole number and a fraction and apply a rule to these kinds of problems.  We brainstormed three of these types of problems.  Then I set them off to work together using any tools in the room to help them (pattern blocks, base 10 blocks, rulers, number lines, paper pencil.)  They worked for about 15 minutes individually and in small groups of their choosing.  At the end of the 15 minutes, some were still struggling with the concept of applying what they already knew to fraction multiplication while others had grasped that and had successfully created a rule.  We debriefed the process and recorded our findings. 

I was very encouraged by this process. I think it gave me hope that inquiry can be an essential element in students better understanding math.  Overall, my students were more engaged in this process than if I had done a mini lesson on the rule then given them time to practice.  I had a student, who generally struggles in math, ask me that if we use repeated addition to multiply, wouldn't we be able to use repeated subtraction to divide?  I had another student think that she had found the rule, but could only apply it to two of our three problems.  After much discussion, where I had to force myself to sit back and NOT say anything, she realized that, in fact, the rule did work, it just resulted in an improper fraction rather than the equivalent mixed number she came up with.  She came upon this by asking questions of herself and her partner, not by having it delivered to her by her teacher (not that I didn't want to.)

I used to think that inquiry had to consist of complex, backward designed lessons.  Now I know that I can approach inquiry as an innovative way to tweak my math workshop where I put the ownness of learning squarely on the shoulders of my students... AND they are totally capable of rising to that challenge.  I also used to think that inquiry didn't have a place in math.  Now I know that it fits into my beliefs about the way students best learn math.

My next step is to have students discover the process of multiplying two fractions in the same way.  I want to see if I can replicate the success I had with this lesson. Another next step, or a missed step, is to assess this process to see how well my students understand how to multiply a fraction and a whole number.

Inquiry about Inquiry

  As a member of "Research Rats", we continue to delve into our inquiry into what needs to happen before, during, and after the Inquiry lessons.  One main thing we have agreed upon is...Although our units of inquiry will be totally unique to our classrooms, they will (and should) follow a "like" process.  In this I mean, certain common threads need to run through all of our classrooms to make all students successful.

 I used to think...Now I think: As I began this unit of "Non Fiction", I began the inquiry cycle by finding out what my students knew and did not know about non fiction.  (See my past post).  From there I began a "mini inquiry" study around the Underground Railroad that I have done for years to combine direct instruction and inquiry into a high interest unit.  As my group has agreed, front loading of  background information and vocabulary along with  immersion via a variety of media sources, and modeled examples of how to create a "researchable" inquiry question within parameters (rather than a free for all) are "must dos" in order for students to clearly understand what is expected of them.  This has worked well for me.  I was able to give up control of my students learning and put it on them without compromising my expectations.

   After some background information and vocabulary were introduced via mentor texts,  students took notes on new background information they were learning.  From there, we made anchor charts that identified their new knowledge, and turned that new learning into questions they had...This proved to be magical as students' questions sparked more and more questions.  As you can see, questions were anywhere from surface level to higher level "researchable" questions.  (I will insert a picture on Monday...unless we have a snow day!  :o)  ).

    From here students were immersed in a variety of media to create more background knowledge and generate more questions in partner groups. (Another picture will be inserted here)

   Where we are now and next steps:   As students created questions, our next step is to determine what a "researchable question" looks like.  It certainly cannot be a "yes or no" question, although this may be a start as the yes no answer can lead to deeper level questions.  This is where we are headed.  Can't wait to see where it goes...

Rookie Researcher

Since others in my group have already stated our goals so eloquently, I will "borrow" their thoughts too...

Our inquiry group is the Research Rats. We are focusing our work around the first two stages of inquiry: Immerse and Investigate. Our overarching question is, “What are the skills necessary for students to conduct successful research during inquiry?” To help us answer this question, we are going to familiarize ourselves with Symbaloo,  a space for teachers and students to add relevant sources. 

I did not bring an artifact to our Friday meeting as I was just delving into my unit and not quite sure what to bring.  As we have just completed a unit around opinion/persuasive writing launching into a unit of inquiry was natural.  During our unit of opinion/persuasive writing the kids had so many questions about why things were the way they were.  After immersing them into several relevant topics through videos, articles, headlines, etc. if was clearly evident these 4th graders had very strong opinions about so many things, and were able to back up their thinking.  Thus we moved into the world of Non-fiction.  I began by again immersing the students into non fiction by having them "explore" various texts, watch videos, etc.  Then we created an anchor chart around their "Noticings" and  "Wonderings" about non-fiction.  The photos below document both what they noticed about non-fiction texts and what they wondered:

I found it interesting that so many kids immediately wondered about source validity, internet, and where authors find their information.  What sources do they use.  Inquiry at its best I would say...It made me realize that my next step is obviously that of exploring how we verify sources.

I don't want to spend a lot of time on these questions (bad I know), because we need to keep moving, but I think perhaps if we spend some time and do a mini inquiry around these questions, we can use them as a springboard into our actual research we will be doing around Colorado History.

I think my next step is to immerse them again into a mini unit of non fiction around a topic of high interest to all.  I am delving into the world of the Underground Railroad this next week.  I will begin with immersing them into this world with a variety of books, videos, articles, etc again and see where it leads us.  I think I have been doing inquiry for years through project based learning and now I am just looking at it more deeply.  We'll see what happens.

The Year of Inquiry, thus far...

Our inquiry group is the Research Rats. We are focusing our work around the first two stages of inquiry: Immerse and Investigate. Our overarching question is, “What are the skills necessary for students to conduct successful research during inquiry?” To help us answer this question, we are going to familiarize ourselves with Symbaloo,  a space for teachers and students to add relevant sources. After recently feeling the roller coaster ride of inquiry, I’m hoping this work will streamline the process for my novice yet eager researchers.

Last Friday I brought a video that one of my groups made for our first round of inquiry.  I was so pleased with ALL of my students' inquiry projects and looked forward to the second round, thinking that I would have the same results.  Not quite...I thought that they did such a wonderful job that I would just let them fly on their own with little guidance.  WRONG!!!  The key is "Guided Inquiry."  I needed a therapy session with Michelle and she helped immensely.  Her AhHa question was, "what did you do differently?"  I came up with a list of things.  I started my third round on Monday and already the scaffolding that I did has made a HUGE difference.  I'm having them make a KWL chart.  Of course, what they know about their question and what they want to know, which are all the questions that they have that will drive their inquiry.  The scaffolding, which gives way to some structure, is wonderful.  I look forward to their projects, with much more guidance.

 Lynn Knowles and I are working on this third round together.  She is teaching the Middle Ages with the 7th grade and the Civil War with the 8th.  Their inquiry will be on their topic they are studying.  At first we thought we'd give them all the same question, "Who has the power, and why?"  The majority of them just weren't grooving on that question.  So I told them that they could come up with their own, that pertains to their history topic, with Lynn and my approval.  They have come up with GREAT questions and are working in earnest, of course with guidance.   

I have really come a long way this year with having the students in rows last year and the majority of the work was done alone to having the desks in groups and inquiry is the driving force.  I feel very comfortable with allowing the students to become responsible and take ownership for their learning 
 within the inquiry groups.  

I am still trying to figure out this blog thing, so when I become more comfortable with it, I will upload pictures and even projects that the students have done.  Stay tuned...

January Inquiry

I am part of the Math Mamas Inquiry group.  At this point, our big question is, "What is Inquiry?"  Our group is composed of all math teachers.  However, since I am new at the whole inquiry thing, I feel like science is a better place for me to start.  Therefore, as I try to answer "What is Inquiry?" I am going approach it through science.

EXPLORE
As Colleen and I started to plan for the 2nd science unit, Weather Systems, we decided to try it as a inquiry based unit.  We started with the overarching question, "How has accurate weather prediction contributed to society's advancement."  I asked students to think about this question and then asked them to share their thoughts and questions. 

As you can see, the students had several questions and thoughts.  However, many of the questions concerned society's advancement.  As a class we discussed what society's advancement could mean.  After several minutes of discussion, I realized I had to focus the discussion on weather and weather prediction.

PUZZLE
The puzzle for me was how to get the kids to ask the questions that we needed answered during the unit.  I noticed that most kids wanted to research tornadoes, hurricanes and major weather systems. 
However, there were many other questions that had to be answer for students to understand weather prediction and society's advancements.   We took some of the big questions from Tracks to help guide the students to create questions that would support the intended learning.

EXPLORE
The major inquiry questions we posed to the students to explore included:
Why are there seasons?
How has weather technology changed over the years?
Why does catastrophic weather occur?
How are elevation and temperature related?
Why do different places in the world have different weather?
How does temperature, air pressure, wind speed and types of clouds influence the weather?
What drives the weather? What is weather?
What makes the temperature of locations at the same latitude different from one another?

Students are now in the process of exploring one of the questions listed above.  They are also creating projects to demonstrate their findings and learnings.

Immersed-Colleen Sechrest

Our inquiry group name is Math Momma's, because we originally came together with a desire to figure out what inquiry looks like within Math.  Our beautiful questions are:  What does inquiry look like? and Why do inquiry?  To kick off our professional inquiry adventure, we have chosen to read selected parts of the book: Succeeding with Inquiry in Science and Math Classrooms.    We began with the second chapter: Why Inquiry? and Why in Your Classroom?  What was reiterated to me while reading this chapter was that inquiry needs to be guided inquiry versus a free for all.

Although our group came together to determine what inquiry looks like in Math, Ms. Schoneman and I started the inquiry process with what seems to be the natural fit, which is Science.  During Friday's PLC, the artifact that I shared was the inquiry Science menu Science Inquiry Menu  that Tracy and I developed. I also brought the wondering sticky notes that each student created.  It was quite interesting that in reviewing all of the wondering notes that they easily fell into categories such as: seasons, catastrophic weather, weather technology, and how do they predict the weather so far in advance.

I think I know that guided inquiry is a great way for students to learn, but I wholeheartedly believe that it must be: very guided, well thought out, well planned, and connected to curriculum standards.  Planning and preparing a well guided inquiry unit takes a lot of time.  I also know that there must be a balance of guided inquiry learning and other teaching methods.  I have some experience with planning inquiry units and based on my experience, I also know that you must be very flexible, because even when you think you have covered all the possible road blocks, there still seems to be a few that pop up.  Through my experience with guided inquiry, I also know that students need a lot of instruction on: effectively searching the internet, how to find good resources, determining the important information, organizing their information, and presenting their findings in a clear and focused manner.

I am still wondering how to best use inquiry in Math at the fifth grade level.  What does that look like?  With so much emphasis being placed on student growth and test scores, I wondering how you ensure that students are learning all the curriculum?  How do you check for understanding with inquiry based learning?  I know that you can check for understanding on the particular topic that a student learns about, but how do you ensure that they have learned all of the content? 

Survivor!

Since Jessica so eloquently expressed our beautiful question, I'll quote her here: 

Our inquiry group is the Research Rats. We are focusing our work around the first two stages of inquiry: Immerse and Investigate. Our overarching question is, “What are the skills necessary for students to conduct successful research during inquiry?” To help us answer this question, we are going to familiarize ourselves with Symbaloo,  a space for teachers and students to add relevant sources. 

The artifact I shared last Friday was a student's slideshow from last year's Survivor! literacy unit.  After conducting this inquiry project with last year's class, I knew I definitely wanted to make changes this year. First, where students worked with partners last year, I wanted students to be responsible for their own learning this year.  Second, I knew I needed to provide more support, a working model, and a rubric for students to clarify expectations.  Third, focused mini-lessons on research and online search techniques are warranted as students can get lost in the web.

The essential questions in the interdisciplinary Survivor! literacy unit are:

• Why is adaptation necessary for survival?
• How does adaptation occur?

Within the unit of study, background knowledge must be activated and schema built through direct instruction. These mini-lessons on content and scientific vocabulary are well-defined and appeal directly to fifth-graders.  After all, who doesn't like to learn about the world we live in, habitats, and animals?

THINK:

Having completed this inquiry unit last year, I learned a tremendous amount about what went well and what didn't.  Students were motivated and engaged not only about the inquiry topic but about being able to choose a habitat and animal.  Last year, time was short, and I didn't provide enough guidance on search criteria.  I'll definitely provide  more guidance this year.  Personally, I have a strong grasp of determining the validity of information on a website and use URL extensions to sift through site choices.  Students do not yet have the experience regardless of the fact that they are "digital natives."

PUZZLE:

My burning question is how much support do you give students.  Clearly they need instruction in both content and research skills.  As teachers we tend to have a hard time releasing control thereby allowing students to make mistakes.  However, a level of guidance is necessary for success.  Do I provide specific websites that I know are kid-friendly but provide useful information?  Do I need to research first?  To what extent do I create a model for them?  What does the rubric look like?  What does successful research look like?

EXPLORE:

My next step is to research high-quality websites along with what is the best combination of direct instruction, scaffolding, and modeling.