Parent/teacher communication is key in and outside of the classroom.  Educators, no matter what level they teach often communicate with parents through face to face conversations, emails, phone calls, and letters.   Generally, elementary teachers type up a weekly/monthly letters to parents informing them of the happenings in the classroom.  This letter writeup has been a staple in many classrooms, including mine.  Depending on the individual situation, more communication from the school can benefit the school community.  Over the past few years new communication methods have started to change the informing landscape.

As they should, parents often want to know how their child is progressing and what’s happening in school.  Keeping community members informed and aware of classroom happenings can create more clarity and demonstrate the learning that’s happening.  This information can also bridge home and school connections.  Beyond the classroom monthly letter, pictures and videos can bring memories and school discussions back home to parents.  This provides parents with opportunities to discuss events and activities that are happening in the classroom. I feel as though this benefits the parent/teacher/school relationship.

I’ve found the three methods below to be valuable in communicating  information to the school community.

Twitter:  Having a classroom Twitter handle has the potential to improve communication with the community.  In an effort to use less paper, some teachers have utilized Twitter to link important documents, such as parent letters, pertinent assignments, homework, and classroom expectations.  I’ve had great success using Twitter to communicate to my stakeholders.  Having a classroom Twitter account can also help engage your parents in using social media.  Twitter also allows two way communication, as parents can send direct messages or Tweets back to the teacher.  If you were ever wondering how to use Twitter in your classroom, visit Lee Crocket’s 60 ways to use Twitter in the classroom.   I should also mention that by setting up your own Twitter account you can also use Twitpic and Vine, which I mention below.

Twitter Example

Twitpic:  A picture is worth a thousand words, right?  Whether you agree or disagree, Twitpic can illustrate what’s happening in the classroom.  Twitpic can also be connected to your classroom/school Twitter account.  Classroom activities and discussions can be documented with the Twitpic app.  A teacher can take a photo with the app and automatically upload it to their classroom Twitter account.  I’ve found that embedding your Twitpic pictures on a class webpage can look like an ever-changing  photo gallery of your classroom.  Parents are able to view the gallery of pictures any time they visit your classroom webpage.  This encourages engagement at home and gives students an opportunity to verbally construct a caption for their parents.

Twitpic Example

Vine:  If a picture is worth a thousand words, what’s a six second video worth?  Some would call Vine a video recording device, but I use it as a communication device.  Vine can connect to your classroom Twitter account.  When parents click on the Twitter Vine link, a new page will pop out that displays the video.  Here’s an article that shows a few different ways to use Vine in the classroom. I’ve used Vine to show how students use math manipulatives, present projects, work collaboratively, classroom arrangements, iPad usage, and many more activities in the classroom.

Vine and Macbeth Example from @morgetron’s class blog

There are many different ways to communicate all the great things that are happening in your classroom.  I just emphasized three in this blog post.  What are you favorites?

* Image credit:  Mim

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:

It’s becoming increasingly evident that technology continues to change the education landscape.  The landscape now consists of a variety of technology tools that teachers can use to facilitate the learning process.  If you look around the field of education you’re most likely going to find more schools that are going 1:1 with iPads (1 2 3) or Chromebooks (1 2 3).  I’ve even heard of schools that are using Kindles or tablets to replace textbooks. It can be challenging to decide what type of technology to order for your school district.  Should you go 1:1 or allow funding for multiple devices in the classroom?  I’m hoping to provide a different perspective on that topic through this post.

I’ve used iPads in the classroom and appreciate the many useful characteristics that they bring to the learning environment.  Students are often engaged while utilizing iPads and the user-friendly interface allows little transition time.  I’ve used iPads for individual math interventions, small group instruction, whole class problem solving activities, and math research.  The fast startup time, battery life, and enormous app selection makes iPads a contendor.  Regardless of all of the positives, I’m still looking for ways to create projects on the Ipad. I believe the iPad is primarily still considered a media consumption device first and a creating tool second.  Maybe this will change in the future?  For project creation involving increased keyboard volume, Flash, precision beyond fingers, and faster processing speeds a laptop/netbook might be a better choice.

Laptops/Netbooks bring additional processing power that an iPad may lack.  Recently my students created a podcast project that could only be completed on a computer.  The iPad has many podcasting apps, but all that I tried lacked the additional features that were needed.  Netbooks also provide opportunities to use open source education software.  This is often not possible with iPads.  From my experience, netbooks often fall short in battery life and startup times, although this is improving.

A document camera brings value to my classroom.  Everyday I use a document camera to display student work and model examples.  My document camera is connected to an LCD projector which displays images on a whiteboard.  Displaying work on the whiteboard and being able to use markers to make corrections or highlight exemplary work is extremely beneficial.  I don’t think I could go a day without using the document camera.

Of course there are many different ways to use technology in a math class.  Relying on only one option (like 1:1) without even considering computers may limit the opportunities for student learning and exposure.  Multiple devices, like iPads, netbooks, laptops, document cameras, tablets, Kindles, and ____ all have different uses.  Understanding how to utlize the technology at the right time is important.  Preparing our classrooms with multiple devices allows students the opportunity to pick the right tool for the project.  I believe we should model, but then give students the responsibility to decide what technology tool to use to complete the task.

What do you think?

Should conformity be the norm?

More often than not, most schools have a naysayer or a group of naysayers.  A naysayer might not necessarily agree with a school’s initiatives or mandates. These staff members are often perceived as being negative or confrontational.  Naysayers might not participate on district or leadership committees.  They might assert their opinions regarding education funding, history of education, evaluations, response to intervention, student data, status quo,  leadership, initiates, etc.   I feel like most teachers have met a naysayer.  You might even be a self-proclaimed naysayer or skeptic.  Naysayers often feed off one another and their ideas can be contagious.

Regardless of how naysayers are perceived, they have power.  I find that teachers want what’s best for students.  Beyond the overarching goal of wanting what’s best for students, teachers’ philosophies differ.   These opinions can start arguments and can cause disruptions among teams/schools.  Confrontations can cause disruptions if not handled properly by administration. Experiences and opinions should be valued and communicated with candor.  Everyone who is part of the education organization is valued and that should be communicated as well.

Being labeled a a naysayer doesn’t have to have a negative connotation   You might be called a naysayer if you aren’t a fan of the status quo in a school or district.  Is that bad?  You might disagree, but being a positive change agent in a school might start by being called a naysayer. Naysayers that bring solutions to the table introduce ideas that may encourage others to innovate.  Conforming isn’t always an option when challenging decisions need to be made. Disagreement may bring a different perspective and initiate a positive change in an organization.  Teacher strengths and ideas may often remain hidden until called upon.  Encouraging naysayers to join school leadership teams and become more involved in the decision making process may benefit your school.

Are you a naysayer?

photo credit: the|G|™ via photopin cc

Different Learning Paths for Different Students

It’s apparent that student achievement data, in many different forms (formative, standardized, norm-referenced, common assessments, etc.) is becoming increasingly valued by administrators and teachers alike.   Teacher PLC teams analyze this data to become more aware of strengths/concerns and differentiate their instruction accordingly.   Instead of whole group instruction, teachers are beginning, or already using guided groups to meet the diverse academic needs of their classroom.

Once needs are identified, teachers put together plans to address the needs in the classroom. Generally, teachers utilize guided reading/math groups, small groups, resource specialists, to meet the needs of individual students, whether the needs are remedial or for enrichment purposes.  One of the goals is to meet the need with some type of teacher support or intervention; although this is not always possible with time constraints and limited staffing.  Have time to be able to individualize instruction is vital for any teacher.  At times, time and staffing limit the amount of differentiation that can occur.  Teachers continue to look for ways to supplement their instruction for differentiation in and outside of their classroom.  Which leads me to this question …

What free online tools can be used to supplement math differentiation in and outside of the classroom?

Note:  All of the tools below are aligned to the Common Core Standards and can be accessed at school or home.  I’m not suggesting that these tools replace school interventions, but they may be helpful if used appropriately.  Click the pictures to enlarge.

MobyMax 

MobyMax is an adaptive online curriculum provider that creates individual education plans for students.  Student take a pre-assessment that seems to be fairly accurate (at least in my opinion).  The pre-assessment determines where to start instruction and helps students practice skills that they haven’t yet mastered.  Student data is collected on every lesson and problem that is completed, so progress monitoring is quite painless.  Mobymax also has an app for easy access.

MobyMax – You can assign specific concepts for differentiation

Scootpad

Scootpad is another adaptive curriculum provider that enables teachers to assign specific CCSS concepts to individual students.  Teachers determine the mastery level and they are able to keep track of individual student progress.  As of right now, there aren’t any lessons associated with the questions.

Scootpad – You can analyze performance on specific concepts

TenMarks

TenMarks is used to introduce or reinforce teaching in the classroom.  Students are able to review online lessons and are asked questions related to the topic.  Teachers are able to track student progress over time with TenMarks.

TenMarks – Lessons are interactive with feedback

XtraMath

Xtramath is designed to help students improve their math computation fluency.  This isn’t a program that’s for everyone.  I’ve found that students who need practice with multiplication/division tables benefit from this web-based intervention.  The program is very user-friendly and has a progress monitoring component which seems beneficial.

XtraMath – Students practice math computation facts

Photo credit: weesen via photopin cc

What tools do you use to differentiate instruction in/out of the classroom?

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 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

Over the past few months I’ve dedicated a good amount of time to to having math conversations. These math conversations occur when the class is unsure of how to solve a problem or when disagreement ensues over what particular strategy should be used to tackle a problem.  The math conversations (or debates) allow students the freedom to openly discuss logical reasoning when solving particular problems.   These conversations can be sparked by the daily math objective or follow another student’s response to a question.  It’s not necessarily planned in my teacher planner as “math conversation” in yellow highlighter, but I do make time for these talks as I feel that they bring value and encourage student ownership.  The conversations also give insight to whether students grasp concepts and are able to articulate their responses accordingly.  Mathematical misconceptions can also be identified during this time.

During these conversations I have manipulatives, chart paper, whiteboards, iPads and computers nearby to assist in the discovery process.  I emphasize that there’s a certain protocol that’s used when we have these discussions.  Students are expected to be respectful and listen to the comments of their classmates.  To make sure the class is on task I decide to have a specific time limit dedicated to these math conversations.  Some days the conversation lasts 5 minutes, other days they may take upwards to 15-20 minutes.  When applicable, I might use an anchor chart to display the progress that we’ve made in answering the questions.  I should also mention that sometimes we don’t find an answer to the question.  Here are a few questions (from students) that have started math conversations this year:

• Why is regrouping necessary? (2nd grade)
• What can’t we divide by zero? (3rd grade)
• Why are parentheses used in math? (3rd grade)
• Why do we need a decimal point? (1st grade)
• When do we need to round numbers? (2nd grade)
• Why is a number to the negative exponent have 1 as the numerator? (5th grade)
• Why do you have to balance an equation? (5th grade)
• How does the partial products multiplication strategy work? (3rd grade)
• Why do you inverse the second fraction when dividing fractions? (5th grade)
• Why is area squared and volume cubed? (4th grade)

Above is just a sampling of a few of the math conversations that we’ve had.  Afterwards, students write in their journals about their experience finding the solution to the problem.

Of course this takes additional time in class, but I believe it’s time well spent.  The Common Core Standards  focus on depth of mathematical understanding, rather than breadth.  This allows opportunities to have these conversations that I feel are beneficial.  They also emphasize the standards of practice below.

• CCSS.Math.Practice.MP1 – Making sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP3 – Construct viable arguments and critique the reasoning of others

Photo Credit:  Basketman

Do you have math conversations in your class?

Education reform continues to make headlines as US student achievement is compared to the achievement of other countries.  An overall increasing focus on standardized assessments has been at the forefront of many of these reform discussions.  Teachers and school districts often get caught in the middle of these types of discussions   From what I’ve observed, what seems to agitate some educators is the notion that one high-stakes standardized assessment can validate/invalidate the success of a school year.  Even though educators have been critical of this notion, federal, state, and local school boards continue to look at standardized assessments as the go-to for quality control/accountability purposes.  I truly feel as though these boards have good intentions, but I would like to encourage them to look at alternative ways to measure school achievement.

I don’t know a teacher that doesn’t believe in accountability.  Teachers inherently feel a sense of accountability for their students.  The way that accountability is being measured and the consequences that occur if growth isn’t met is what’s causing concern.  Critics emphasis that only focusing on standardized test scores encourage teaching to the test, massive amounts of test prep and unfortunately cheating.  I’m not downgrading the value of standardized assessments as I believe a limited amount are beneficial in providing valuable feedback that can inform instructional decisions.  Appropriately utilizing student assessment results may prove beneficial for a teacher or school, but using that data outside of its context to manipulate accusations can cause problems.

Proactive Steps …

By now most educators have realized that student achievement data is starting to make up an increasing portion (20% + ) of one’s evaluation.  In some cases one VAM assessment could be used to measure student growth and impact employment decisions.  Instead of using one standardized assessment to determining teacher effectiveness, administrators should enable teachers to show student learning through a variety of means. This is a difficult task to tackle as administrators are also being assessed on standardized assessment results.  While one assessment shows a singular brush stroke of learning, the picture becomes much clearer when multiple data points are used.  Even NWEA, the makers of the MAP assessment encourage school leaders to use multiple data points (not just MAP) to measure student growth.  Regardless, some districts are already using singular assessments for evaluation/employment purposes.  I’m advocating that principal’s take a closer look at multiple student achievement data points instead of relying on one growth indicator.

How …

Formative assessments, student projects, presentations, and pbl activities can show learning at varying levels.  This collection of student data can not only help inform instructional decisions, but show evidence of student learning.  Digital portfolios are making a splash in education and I’m hoping that more districts start using them in conjunction with standardized assessments to provide evidence of student learning.  Showcasing student learning through a variety of formative assessment tools gives more meaning to the learning that’s happening. If communicated appropriately, state and local schoolboards will take notice and become more interested in multiple data points to determine effectivenessss, rather than a singular one.

photo credit: CliffMuller via photopin cc

A few days ago I started gathering resources to supplement a math unit on fractions.  The classroom was studying equivalent fractions and I thought there might be a variety of resources available on a few of the blogs that I regularly visit.  I generally follow the #mathchat hashtag  and find/share ideas that relate to mathematics.  While reading a few math blogs on fractions, I came across John Golden’s site that has some amazing ideas that can be used in math classroom.  His triangle pattern template sparked my interest.

John provided a template that’s available on his site.  I printed out the template and began filling out each triangle with fractions.  I ended up with a sheet that looked like this.

A template of this can be found here.

So what happened?

First a lot of brainstorming and error checking.  Then I decided to have students cut out the triangles and compile equivalent fractions.  This is what happened …

Students in fourth grade cut out each triangle and combined them to make equivalent fraction squares.  Students worked in collaborative pairs during the project.  I observed students using math vocabulary and having constructive conversations with each other to finish the assignment.

Before giving the assignment to a fifth grade class I decided to eliminate two triangles on the sheet above.  It was the job of the student to find what triangles were missing and create equivalent fractions to complete the squares.  The students were engaged in this activity from start to finish.  Some students even wrote the equivalent decimal next to each square.

Overall this project took approximately 45 minutes to complete and it was worth every minute.  Students used the terms fraction, improper fraction, mixed number, numerator, denominator, multiplication, division, and pattern throughout the project.

Just as I did, feel free to tweak this project to best meet the needs of your students.