Taking Math Outdoors

Math Outdoors

Recently I had an opportunity to attend an outdoor education trip with our elementary students. The trip took place over three days and was located in a very remote part of the state, away from high rises, city lights, cell phone signals, and televisions.  The trip focused on learning about birding, forest ecology, Native Americans, orienteering, and pioneering.  For many students this trip is a different learning experience.  It’s outside of the classroom and therefore a different learning environment for them. Acclimating to this environment took a bit of time for staff and students.

The adults were responsible to teach many of the concepts during hikes on campus.  Being outside is a great opportunity to introduce or highlight academic concepts that are generally taught through abstract means.  While talking about math outdoors, students expressed interest and asked questions that often led to additional mathematical questions.  Students that might not usually be fully engaged in a math lesson at school were shining on the hike. This experience led me to reflect on our current mathematical practices.  At times there’s a disconnect between what’s happening in the classroom and what’s occurring right outside of the doors to the school.  Teachers often attempt to bridge the gap, but self-directed student questions often come from real world experiences and curiosity.  Curiosity is often followed by questions.  Finding answers to those questions can lead students to find their passions (eg. #geniushour).  This motivation can be encouraged but not genuinely bought or sold.  Students decide how engaged they want to be and internal/intrinsic motivation often leads to learning experiences.

Below are some (of what I can remember) of the questions/topics that were discussed while on the trip:

Concepts

			

Letting Students Decide

You Decide

Last week I decided to introduce one of my math classes with a complex algebra problem. The problem had multiple solutions and a variety of different ways to achieve the answers.  I grouped the students and they began to discuss methods to solve the problem. Each group was given an iPad, whiteboard and marker to get started.  After approximately ten minutes I had group coming up to me asking if they were on the right track.  I asked the students to decide on what path to take to solve this problem. The students waited for additional instruction but I decided to say no more. Often, students are looking for affirmation or some type of hint.  I told the students to rely on their math skills to validate why they think their solution is best. The students went back to their group and continued to work and validate their reasoning.  Students continued to have questions and I decided to answer those questions with questions that pointed students in the right direction. By facilitating and guiding I felt as though students were taking more ownership of their own learning.  After approximately thirty minutes student groups presented their answers to the class.  The majority of groups indicated that they hit multiple roadblocks, but eventually achieved some sort of success in finding a solution to the problem.  After listening to the presentations I concluded that the students took another step this year towards becoming responsible learners in the classroom.  Moreover, I found myself reflecting on what was communicated to the students during the process.

The words you decide can be powerful.  In a classroom setting, the words can enable students to make decisions that impact their learning.  Students need to be able to take ownership of their own decisions and what a teacher communicates can benefit or limit learning in the classroom. I’d like to move my students beyond the stereotypical systematic focus of finding the one right answer.  Mathematical understanding might not permeate when students feel that finding the answer is the only goal.  Giving students opportunities to make decision within a safe environment prepares them to own their own learning and become more accountable in the classroom.

What strategies do you use to encourage student ownership?

Photo Credit:  S. Miles

Student Groups and Debates

Student Group Dynamics
Student Group Dynamics

Teachers often have students work in groups to solve problems.  Educators may recite that “two heads are better than one” or something of that sort when talking about the power of effective collaboration.   I’ve seen firsthand how student grouping can impact decision making and student learning.  How a group interacts will often influence outcomes.  Positive interactions between group members often spurs a team to meet their goals.  I believe most teachers encourage positive talk during group activities and many set up a norm/expectation list for behavior. Learning is often stretched when students are encouraged to explain their answers to others.

What happens when a student explains an answer and the other party isn’t receptive?  Or, what happens when students disagree on an answer or how to solve a problem?  This is bound to happen from time to time, but I don’t think this is necessarily a negative.  Students should be able to stay on topic and analyze their own argument without expressing frustration towards the idea (not people) that they disagree with.  Disagreement may conjure anger if not carefully managed.  This requires clear expectations and modeling by the teacher. Easier said than done?  Yes.  Often “I agree” statements can overshadow academic misunderstandings, while students just follow what the leader is saying in the group.  I’m aware that some classrooms encourage debate and I think that in some cases that benefits the classroom.  I should also note that having a classroom/group debate depends on the problem and is purely situational.

Students, no matter what their age, need to be able to communicate their ideas in order to meet goals.  It’s perfectly fine for students to disagree with the group.  How that disagreement is communicated and received charts the course for the group.  Individual insights hold value and each contribute to the overall goal of the group.  Students need to be able to disagree respectfully, but understand that the team is working towards the same goal.  Students that have this mindset are able to offer differing opinions, but innovate as a team.

Having a balance is key.  Groups should work together but also be open to differing ideas. Disagreement often forces other students to justify their positions.  Justifying provides opportunities for students to analyze their own argument, which gives the teacher a better understanding of a student’s understanding of a particular topic/concept.

I think this also plays a role in how adult teams operate as well (see Ringelmann).  I’m going to end this post with a quote from James Surowiecki, the author of The Wisdom of Crowds.

“The wisdom of crowds comes not from the consensus decision of the group, but from the aggregation of the ideas/thoughts/decisions of each individual in the group.”

 

Picture Credit:  S. Miles

How Do You Measure School Achievement?

School Achievement


Student achievement is often at the forefront of the minds of school leaders. Achievement, in the form of student data, inundates schools, teachers, and school improvement plans.   Moreover, school improvement plans seem to hiccup when state assessment results are released.  This data is generally looked at in the form of numerical values related to student achievement on state standardized assessments.  If utilized correctly, analyzing student data may be beneficial for a school/district.  Reviewing strengths and concerns may help allocate resources to areas of need.  Regardless of the benefits, some school leaders and teachers often focus on the need to raise test scores in order to receive a positive rating from the state or district.  That pressure can lead to anxiety and fear as student data is now being tied to teacher/principal evaluations.

I believe school achievement can be viewed through a variety of lenses.  Even though the nation doesn’t necessarily measure the traits below,  I feel that they are still valued.

Character

How well does your school emphasize character?  Some schools use programs, such as Character Counts, while others have deployed their own character curriculum. Discussing anti-bullying strategies and positive ways to cope with problems can be contained within this category.  Emphasizing positive character traits can contribute to becoming more responsible in and outside of the classroom.

Reflective Thinking

Are students allowed time to reflect on their own learning?  Students that are given opportunities to review their achievement/behavior/study skills may set appropriate goals to better themselves.  This skill will be used throughout their life. Is goal-setting important in your school?  Can students analyze their own achievement and create appropriate goals?  Setting and achieving goals often brings confidence and focus.   Goal-setting can be emphasized at any grade level.

Creativity

Does your school allow time for students to be creative?  Does your school offer opportunities for students to be curious?  Are student assignments geared to offer one solution or multiple solutions?  I’ve found that curiosity often leads to creative thinking. Creative thinking is difficult to measure, but the value is immense.

Requesting Feedback

Allowing feedback gives opportunities for stakeholders to offer input regarding changes that may benefit the organization.  How the feedback is utilized may possibly advance a classroom/school/district’s vision.  Using the feedback to better an organization shows value.  Data in the form of feedback can be just as valuable as standardized assessment data.

Collaboration

Does your school encourage collaboration?  Collaboration between staff, or collaboration between students?  I would think it might be both.  Is the classroom environment conducive to collaboration?  Working together also encourages students to practice positive character traits.


I understand that not all of the skills above are measurable   Understanding that school achievement goes beyond standardized assessment results is a step in the right direction.

photo credit: sabeth718 via photopin cc

What do Schools and Libraries Have in Common?

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I recently retrieved a reserved book from a nearby public library.  I’m amazed at how libraries have changed over the past few years.  Some of these changes have been welcome and encouraged by communities. The notorious Dewy Decimal system has been simplified with an online catalogue, silence is now not expected in all parts of a library, librarians have become “media specialists”, online research is becoming the norm, etc.  I could go on and on about the changes in the local library, but I’ll stop here.

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This particular library  that I went to visit has rows of computers, an ebook reading zone, two copy machines, reservation rooms, DVD/CD check out, moveable furniture, and a ton of space for collaboration.  The library has recently been renovated to improve access for patrons. There are study corals for people who need to work independently and reservation rooms for group discussions.   A technology corner includes headphones and laptops available for checkout.  I could tell that the designers intentionally created certain parts of the library for group collaboration.  Those zones have electrical outlets, moveable furniture, and wifi access so that work can be optimized.  After leaving the library I started pondering to what extent the library design could be replicated in a classroom setting.

Just as the library environment encourages literacy, the classroom environment plays a pivotal role in limiting/enhancing how students are able to collaborate and learn. I started to reflect on the questions below.

How does your classroom environment enable or encourage collaboration?

Is there an area that is designed for independent work?

Is technology easily accessible for student use?

Is there an area that is designed for research?

I believe that it’s important to ask the questions above and seek answers.  The classroom environment should promote collaboration and give students opportunities to learn in different ways.  Moving beyond the single row classroom setup encourages students to take ownership of their learning.  Giving students opportunities to learn without desks or in a student centered environment may prove beneficial, as some studies are beginning to indicate.  Allowing a bit of flexibility in a classroom setup can reap dividends later on in the school year.  If the library can reinvent itself, I believe a school/classroom can do the same.

photo credit: j l t cc
Liz508  cc