Homework and Learning


Homework has been a contentious subject in the field of education.  Many people in education have been/are willing to talk about the subject; see examples 1, 2, 3.  Beyond the annual science fair and occasional project, homework in elementary school is generally used to practice or reinforce skills learned in school.  Reinforcing skills through application is important, although the homework that is often assigned at the elementary level tends to be worksheet based.  I’ve found this to be especially evident in math classes.  Beneficial math homework has value and can extend the learning experience.  I’ve observed some amazing educators assign math homework that stretches their students’ thinking.  I believe that this type of homework isn’t the norm, although I wish it was.  At times, I’ve seen math homework being used as a motivator, but there are definitely myths related to homework. Some teachers use homework as part of a student’s grade.  This can be problematic, as the environment outside of school can play a role in whether the homework is done and if it’s actually accurate.

Adam @agholman wrote a Tweet that seemed to be spot-on when talking about grades.  I connected the Tweet below with the idea of homework and motivation.

“But they won’t do it if it’s not for a grade” – This tells me way more about your motivation than your students’

As soon as I read the Tweet I started asking questions …

  • So in theory, one way that educators can encourage students to complete homework is to assign it with point values attached?
  • If a reduction in a grade is based on incomplete homework, does the grade really reflect mastery?

I believe that rewarding/punishing students for doing/not doing their homework can limit motivational tendencies in and outside of the classroom.  Can a teacher truly validate that a student should receive a “C” instead of a “B” because of homework issues?

Now … for some students homework fulfills its purpose.  Students practice and may receive help, but through the practice they are improving in their understanding of certain concepts. This can be beneficial.  As educators already know, this is not the case for all students.  Students that don’t complete the homework on time or turn it in may need some type of intervention in the form of extra help or possible enrichment, depending on the student.

Grading homework in itself can be a form of feedback, but purposeful direct feedback can help students understand concepts more clearly.  Unfortunately, many students don’t look beyond the grade on their paper for feedback.  There isn’t an easy answer for this problem, but I believe moving towards standards based grading practices may help in this situation.  An emphasis on formative assessment practices and feedback may also provide value.  Written feedback with a self-reflection component can be especially valuable in enabling students to become more responsible for their own learning.

My Takeaways:

  • Homework may benefit some students, but definitely not all
  • Grading homework doesn’t necessarily increase motivation or accurately reflect understanding
  • If you’re required to assign homework, assign meaningful and relevant homework
  • Direct feedback (not the actual grade) on formative assessments/homework continues to play an ever important role in the learning process

photo credit: bgilliard via photopin cc

Releasing Control

In a matter of weeks schools will be opening in my state and across the nation.  Most students and teachers are anticipating a smooth start to a new school year.   For me, this summer has been full of opportunities to hone in my teaching practice and expand my PLN.  Reading Teach Like a Pirate and attending Playdatedg58 were two opportunities that stretched my thinking in preparation for a new school year.  This post is based on what I’ve learned through these events/activities.

1. Teachers have control (for the most part) and can take risks in the classroom

The experiences that I highlighted above have brought insight to the idea of teacher control in/out of the classroom.  Teachers  often have more control in their classroom than many educators would like to admit.  Besides the curriculum given to the teachers by administration, how much input do teachers have in how their classroom is constructed/run?  Speaking from an elementary teaching perspective, teachers have quite a few opportunities to modify their classroom environment.  Middle and high school may be a bit different as more than one teacher is in one classroom throughout a day.

The concept of instructional academic freedom often gives teachers the ability to teach how they feel best engages students in the learning process.  Of course this depends on how academic freedom is interpreted.  The book Teach Like a Pirate has reminded me that educators can take risks in their classroom.  Trying out a new teaching strategy can bring fruitful results.  Creating lessons that with unique hooks can engage students in new and exciting ways.  Students are more likely to retain and apply knowledge when their learning experiences are memorable.  Moving outside of general lesson plans that are often created by publishing companies, gives teachers the ability to differentiate lessons based on students’ needs. Engaging lessons might include lots of conversations, noise, excitement, wonder, curiosity, disarray … but also learning.  This may not always the norm in your building or school but I feel that action is needed to move beyond standardizing all schools, classrooms and students.

Now, I understand that not all teachers feel this way.  Some are in organizations that mandate specific teaching protocols that may limit teacher academic freedom in the classroom.  Also, some teachers may feel that they are unable to take these types of risks in the classroom because of expectations from administration.   If you find yourself in a situation where taking a teaching risk isn’t the norm, feel free to speak with your administration about the benefits of your idea.  Within reason, most administrators will support the enthusiasm and ideas that a teacher brings to the table.

2.  Give the control back to the students

Many of the teachers that I met at Playdatedg58 seemed to feel comfortable creating engaging learning opportunities for their students. I’ve found that most teachers want students to become intrinsically motivated to do their best. That motivation is vital in enabling student ownership in the classroom.  I’ve found that materialistic motivators to be less than stellar in developing student ownership.   Moving beyond materialistic rewards also communicates that some of the satisfaction gained from learning and accomplishing tasks is internal.

I remember being a student and rarely having input in classroom decisions.  It was informally communicated that the teacher was in control of what/how I learned, resulting in close to zero student ownership.  The near 100% teacher direct instruction didn’t help my situation. Fortunately this changed for the better as I progressed through elementary school.  I believe that giving students the opportunity to make decisions in the classroom is important.  It also communicates that the teacher has created an environment where there is trust between the students and teacher.  Creating that climate of trust is essential for student ownership.

How do educators create an environment where students feel comfortable and are encouraged to take ownership of their own learning?

Keep in mind that this list is designed for elementary students, but I’m sure it could apply to other grade levels.

Students are given opportunities to  …

  • Make classroom decisions – rubrics, what problems/assignments to complete
  • Set expectations – set rules for class
  • Set goals – analyze their performance, set personal goals, monitor progress along way
  • Give/offer feedback – use plus/delta, quality tools, reflect and offer input regarding learning
  • Publish their writing – use blogging platforms to publish/scan in digital works
  • Use social media – Tweet , Vine, Instagram, Twitpic throughout day/week/month
  • Participate in Student jobs – electrician, technician, paper passer, etc.
  • Journal – reflect on progress made and respond to written feedback by teacher
  • Setup the classroom – help in arranging classroom setup
  • Respectfully debate – participate in conversations about most effective way to solve ______.

I believe that a classroom is a community of learners.  To accomplish some of the tasks above teachers need to be able to step back and give students opportunities to take control/ownership. Many new teachers that I’ve encountered feel that if they allow students opportunities to express themselves they won’t be able to regain control and that will negatively impact their evaluations. I’m sure many educators have heard the sarcastic phrase “don’t smile till January” or something like that.  I’ve found that giving students opportunities to control their learning also benefits the entire classroom community.  Giving up some control in the classroom means that educators are willing to take a risk and create a classroom environment that enables students to take responsibility for their own decisions.

4 Ways to Encourage Student Self-Reflection in Math Class

Math teachers have a variety of tools that can enhance the learning process.  Technology, math manipulatives and problem-based learning activities can all play an important role in a math classroom.  Regardless of the tools or strategies, one of the most powerful motivators that I’ve utilized over the past few years deals with the concept of reflection.  Adults often learn by experiencing events and reflecting on them later.  Generally the reflection lets us make better or more informed decisions in the future.  Many educators blog, which I believe is one form of reflection.  Allowing students opportunities to reflect on their math learning experiences, including celebrations and mistakes can be time that is well spent.  A sense of ownership develops when students begin to understand that their success isn’t only dependent on the teacher or tools within the classroom, but on themselves as well.  Reflection is especially powerful after making mistakes.  By reflecting on math mistakes, whether they are procedural, formula issues, or simple errors, students become aware that mistakes are part of the learning process and shouldn’t be on the taboo list.  How do we give students opportunities to reflect in math? Here are four possible ideas:

  • Math Journals – This is a great way to gauge a student’s understanding of particular math concepts.  I’m continuing to find that students are using their math journals to communicate their conceived strengths and personal concerns.  Students are asked to reflect on their learning experiences in the journal through various journal prompts.  I check the journals periodically and am able to provide feedback to individual students.
  • Student Led Math Conferences – Throughout the year I have personal math conferences with the students.  Students bring their formative assessments to the conference and the student reflects on their progress.  We work together to find areas that need strengthening and write a personal goal related to specific academic concepts.  Students may decide to bring their math journal to their math conference.
  • Class Anchor Charts or Plus/Delta Chart – After a formative assessment or test the class may have a discussion about what problems on the assignment caused concerns.  We then reflect on the processes used to find the answer and have a thorough discussion about the mathematical process.
  • Blogging – Student blogs allow time to reflect on their mathematical process.  Students can blog about how they solved a particular problem and what steps were needed.  I find that blog explanations are especially useful when explaining solutions to problem-based learning activities.  It’s also a stellar documentation tool.   Keep in mind that the blogs may be public and not all students want to wave their mistakes in the air.

photo credit: doctor paradox via photopin cc

How do you encourage student reflections in math class?

Student Self-Reflections

photo credit: karola riegler photography via photopin cc

Over the past few years my teaching practice has evolved.  Growth in the teaching profession often occurs through experience and professional development.  As continuous learners, teachers generally hone in on their craft over time.  I believe reflecting on teaching experiences plays a role in the professional growth of an educator.

  • How often are teachers able to reflect on their craft?

I’d hope that it would be more often than not at all.  Personally, reflecting on past experiences can lead to better decision making and goal setting in the future.  They’re many ways in which educators can reflect.  Off the top of my head I can think of:  after a professional development session, reading or commenting on a blog post, participating in an education twitter chat, attending workshops, and many more.

  • If educators feel that reflecting on experiences is important, why not give students opportunities to reflect on their progress?

Absolutely.  One way in which reflection has been beneficial in my classroom is actually rooted in the formative assessment process.  Local formative assessments give quality information that can be used to drive instruction in the classroom, while other data (standardized assessments) are used for district/state/nation purposes.  Formative assessment data not only serves the teacher, but it also informs students of areas of strengths and concerns.  Last year I decided to have my students use a reflection journal to analyze their own achievement levels in class.  Students reviewed their formative assessments, usually in the form of exit cards, and wrote a short paragraph regarding how they performed.  I asked the students to write a few sentences related to how close they are in understanding the concepts observed on the exit card.  Every so often, generally after a grading period, students were guided to setting individual goals for themselves. These goals were based on the journal entries and learning experiences throughout the grading period.  This process required modeling during the introduction phase, but after two grading periods the students were ready to complete this independently.

I vaguely remember using journals during my K-12 experience.  The teachers that assigned the journal entries rarely wrote any comments back to me.  This peeved me as a student and I’m over it still does as an educator.  Therefore, I make a conscious attempt to review all the student reflection journals and write short individualized comments to the students.  The comments show the students that their teacher is aware and cares about their progress.  This action is especially important to students that might not be as assertive in class or might be embarrassed to state how they truly feel.  I place an emphasis on the student created goal. Student goals are highlighted  as I will often share them with the parents to ensure that we’re all working towards the same end goal.

I also find that the student reflection journals show student growth on a personal level.  When growth is evident, students often gain confidence in setting new goals.  Reflecting on progress made can be a tremendous opportunity to set goals.  These goals can empower students to own their learning.

Side note:

 Reflections can take on many different forms.  Incorporating various prompts throughout the entire school year also communicates to the students that goals don’t have to be directly associated with scores.  In the past I’ve used field trips, current events, literature, and problem based learning activities for reflection journal prompts.  

* Feel free to visit Helen Barret’s reflection for learning site for more information on this topic.

Using End of Year Classroom Survey Data

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For the past few years I’ve used a student motivation survey with my class.  The survey is used for reflection purposes and to plan for the next school year.  This year approximately 80 students in grades 3 – 5  answered questions related to what helps them learn best.  The statements are below (click picture to enlarge).


I usually explain each question to the class and then the students  individually respond as they see fit.    After the results were compiled and averaged (1 being the most important, 10 being the least), I shared the top three motivators.  They are as follows:

  • The teacher shows she/he cares about you and the other students in class – 1.20 / 10
  • The teacher is fair to all students in the classroom – 1.22 / 10
  • The teacher allows you to use technology to learn – 2.02 / 10 

After the results were presented, the class had a discussion regarding why they felt the motivators were especially important.  I also shared that the results were very similar to last year’s results.   One key takeaway was that having a teacher that cared about them was extremely vital in motivating students to learn.  This isn’t surprising, but a passionate teacher can be contagious and elementary students often feed off of that excitement.  Another takeaway, relationships matter in the classroom.  Also, it seems that technology continues to play an increasingly important role in the learning process.

I then presented the bottom three categories.  The bottom three aren’t necessarily negative, but they scored the least important out of all the categories. The class then discussed why they felt like those categories deserved a less than stellar score.

  • The teacher gives choices to complete an assignment – 5.51 / 10
  • The teacher allows you to move around the classroom – 4.43 / 10
  • The teacher gives assignments that connect to the real world – 3.53 / 10

At that point I thought it might be beneficial to bring up the topic of motivation and rewards in the classroom.  This year I decided to eliminate material rewards (pencils, stickers, auctioned prizes, etc.) to reward my elementary students.  It took some research and a bit of teeth grinding, but I went cold turkey with the external rewards this year.  This was a shift from years in the past.  After analyzing the positive results and increase in student ownership, I may do the same next school year.

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

Math Debates in Elementary Classrooms

Learning through Conversations

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?

What do Schools and Libraries Have in Common?


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.


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

The Value of Self-Correction and Student Ownership

This year I’m continuing to find that student ownership plays a critical role in the learning process.  Students often become more responsible for their own learning when they are given additional opportunities to show their learning.  I’m finding that part of the key to increasing student responsibility depends on how it’s communicated by the teacher.  Students can’t be expected to own their learning without any guidance.  The gradual release of student responsibility can benefit the overal climate and achievement of a classroom.  In the past, I’ve used student journaling, plus/delta, surveys, choice boards, self-selected research projects, and other strategies to promote student ownership.  This past week I introduced another strategy that involves self-correction.  Here are the steps:

1.)  Students complete an assignment in collaborative groups or independently.

2.)  Students finish the assignment and self-correct using the Teacher’s Manual.  This can also be applied to digital progress monitoring tools.

3.)  Students independently use markers to indicate wrong/right answers.  If needed, students will write in correct answers.

4.)  Students utilize their math journals to reflect on the assignment and their feelings about the topic and achievement.

5.)  Student turn in their paper and journal to the teacher

6.)  Optional:  Students use multiple journal entries for individual goal setting

It might seem simple, but I’ve had terrific results from using this strategy.  Overall, I feel as though the students benefit from practices like this.  The self-correcting / journal process took modeling and practice at first, but the benefits are starting to become apparent.

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