Category: Elementary Teaching

Estimation Challenge

Image by:  Akeeris

Over the past few years, I’ve been working on ways to utilize technology to improve student learning.  Understanding what objectives are being assessed helps me plan on what technology will be used and in what capacity it will be used.  One of the second units in my class emphasizes the importance of estimation.  The fifth grade Chicago Everyday Math curriculum asks the students to do the following:

Notice that the question says “location given by your teacher”.  Instead of giving all the students a specific destination, I decided to have the students pick an establishment (Culvers, Kohls, local park, school, etc.) in the town that they reside.   In the past, I’ve found that student choice can be a motivator for students. The destination had to be within 15 miles of the school.  The students were grouped in triads and were given a computer to complete this task.  Students were asked the following:

  • What is your destination?
  • About how many miles is it from your school to your destination?
  • About how many steps will it take to reach your destination? (they used the conversion in the journal above)
  • How long would it take you to reach your destination?
  • What breaks would you take during your walk to your destination?
  • If you left at 8:00 AM on Monday, when would you arrive at your destination?

The students were also given the Google Maps website to start their estimation challenge.  Most students were able to navigate Google Maps and find the “get directions” tab and enter in the school address.  The groups were able to find the establishment address fairly quickly, although some groups needed prompting.  The student groups needed to find out what route to take to their destination.  Some routes were quicker than others, but involved a lot of stopping at cross walks.  Other routes were scenic, but took longer.  Each group decided which route to take and found the Google Maps distance to the destination.  Here is a sample of what the students were looking at:

Some of the groups extracted the “Google Maps time” to answer the questions. Other groups thought that it seemed odd that it would take a specific amount of time for everyone to reach the destination at the same time.  One of my students remarked that not all people will take 2 hours and 56 minutes to reach the destination. I thought this was a prime opportunity to bring in the topic of ratios and proportions. One of the groups decided to time themselves walking 10 feet and then find out how long it would take to walk an entire mile at that pace.  I was impressed with the groups that went beyond the artificial time given by Google Maps.  Even more, the topic of ratios and proportions is typically introduced next school year.

Near the end of the project, the students presented their answers to the class.  Each group chose a different location and I could tell that their answers were well thought out.  Overall, the skills utilized in this project are applicable outside of the classroom and I feel that the students were fully engaged and met the objectives for the lesson. This is one of the projects that I’m planning on using next year.  This is my second Google Maps activity, my first lesson can be found here.

So You’ve Been to a Common Core Training?

The words above seem true.  If you work in education, you most likely have heard about the math Common Core Standards.  Many educators have been given instructions and maybe even have had the fortunate experience of attending a PD session on the Common Core.  According to WAT, approximately 70% of teachers have received some type of Common Core training.  Maybe your district now has a Common Core “aligned” curriculum or manipulatives that will be utilized in the classroom that emphasize the main points of the Core?  Regardless of your situation, the content that you teach may be impacted by the Common Core Standards.  Many educators/administrators are asking questions about the Common Core and seeking answers on their own.  Common Core PD sessions have allowed teachers opportunities to ask questions and receive clarification on what is expected.  Here are a few statistics:

If you are like many educators, then you’ve been trolling to find additional information about the Core and resources that will enhance your instructional practice.  I’ve created a list below that may help us (as we are all in this together) unravel the Common Core and the changes that it will elicit over the next few years.  The links below aren’t listed in any prioritized order, but they are categorized to help you (and me) find and use the information quickly.  I have many of these sites already bookmarked, as I receive questions on the Common Core and it’s far reaching impact.

Blog Posts:

General Info on the Common Core:

Livebinders / Digital Newspapers:

Testing Questions / PAARC / Behind the Scenes:

“Aligned” to the Common Core

Image by:  Felixico

Now more than ever it seems that educational leaders are being encouraged to align their curriculum to the Common Core. Currently, 45 states and 3 territories have signed the Common Core initiative.  National tests are now being developed to evaluate how well students understand the math and reading Common Core standards.  Seeing that the majority of the United States supports the Core, new “Common Core Aligned” products seem to be popping up everywhere. Workshops, seminars, webinars, and PD sessions are dedicated to communicating how the Common Core standards impact curriculum.  In general, I believe that the workshops mostly benefit teachers. I also believe that the Core will give opportunities for educators to positively change the way that they deliver math and reading instruction. What I’m concerned about though is how the “aligned” resources are being utilized.  I in no way endorse/oppose the products below, but the images & links contribute to the notion of how publishers (McGraw Hill, ASCD, Pearson, etc.) are marketing Common Core resources to educators and administrators.

I’m finding that teachers are being pressured into purchasing these “aligned” materials to prepare their students for the upcoming accountability testing.  I’m not against the Common Core materials being produced or used in the classroom.  I’ve actually read many “aligned” resources and have found them most beneficial.  To be honest, most educators that I know have already viewed a number of the Common Core materials.

Don’t get me wrong, educators should be aware of the new standards and adjust their instruction accordingly.  The over reliance on “aligned” published materials can cause teachers to take less risks as they focus only on items located in specific published books.  In these cases differentiation may occur less as the teacher uses whole group Common Core instructional techniques to cover specific content that’s found on future standardized assessments.  I view the “aligned” resources as important and another tool in an educators tool belt.

“Aligned” materials and other supplemental materials should not be viewed as a magic bullet in raising test scores or in teaching in general.  Instead of impulsively purchasing “aligned” materials, school districts around the country should collaborate with each other to share resources that will benefit all stakeholders involved.  I believe some states are attempting to use this model and I applaud their efforts.

Utilizing teaching strategies that work for educators and their students instill an appreciation for learning and give students an opportunity to show their learning in new settings.  Using solid pedagogy along with supplemental resources allows teachers to differentiate their instruction to meet the needs of all students.

Differentiated Instruction

Image by:  Grant Cochrane

Lately, I’ve spending time preparing for the 2012 – 2013 school year.  Last week I had a conversation with a teacher in another district about student achievement data, specifically MAP data.  We discussed similarities/differences in general student achievement data.  The achievement data inside a typical elementary classroom can range significantly.

This data along with teacher input can bring awareness to academic strengths and concerns.  Educators are responsible for teaching all students regardless of prior knowledge.  I think most stakeholders would agree that prior academic background knowledge vastly impacts instruction and pacing.  What happens if that prior knowledge is missing, partial or incorrect?

All students in a classroom should have the opportunity to experience success.  That success depends on the environment and instruction that occurs throughout the school year.  What do teachers proactively do to meet the needs of all students in their classroom?  Treating all students to the same instruction, same assignments, assigning same goals, same homework, same _____ doesn’t help all students meet their potential. I’ve found that differentiating my instruction is one way to meet the diverse needs of students.   What does differentiation look like in the classroom?  “Differentiated Instruction is matching instruction to meet the needs of individual learners ” –FCRR.  I’ve included strategies with links for more information on differentiated instruction below.

The links below have been helpful in writing this post.

Gifted Differentiation  GT Webinar  Instruction for Gifted Learners  Flexing Differentiation Ideas for Teaching

Planning – What plan?

Image by:  Stuart Miles

I remember approximately ten years ago  …  my school just received the opportunity to utilize classroom webpages.  Instantly, I thought that posting class letters, general information and homework on my class website would benefit the community.  The webmaster at that time told the staff that we were only able to update the pages once a week.  I’m not sure why, but I assume they wanted to slowly roll out this “new” technology.  I naively thought that I could just post a weeks worth of homework on my webpage on Monday and just update it on the following Monday. To say the least, my idea needed extreme tweaking. By Wednesday of that week, I was finding myself behind the homework schedule.  I was definitely finding out that my plans were not working. Around the third week of school I decided to utilize my homework idea later. After much reflection and having to explain myself numerous times, I would consider my webpage homework situation a learning experience.

Fast forward nine years later –>

Last year, I tentatively placed specific academic units in certain months and time periods in my planning book.  I used pencils with this because inevitably there are always edits to the schedule.  As the year progressed, my eraser was definitely getting its use.

These eraser marks/edits are often the caused by variables.   Scheduling conflicts and students are just two of the variables.  I appreciate the fact that students are a variable in the classroom.  Why?

Not all students learn at the same rate or the same way.  I tend to emphasize this concept during community interactions.  Advancing through the curriculum at an accelerated pace doesn’t necessarily mean that students understand and are able to apply their learning. Accelerating curriculum may mean that some topics are lightly coated.  The learning experience can be impacted (positively/negatively) through acceleration.

Now –>

I’m not advocating for less planning, but instead, I feel that educators need to tentatively plan their instruction and communicate that the pace and lesson sequencing may change.  I’ve already purchased my official school planning book for the fall and have started to sketch in a few key dates.  I’m just about ready to start mapping out the curriculum for the year.  Before writing any curriculum events, I always remember my homework situation in the first paragraph of this post.  That humbling experience has allowed me to be more proactive in setting realistic goals for students to learn and (more importantly) apply their learning.

Educators can plan until their heart is content, but their plans will not be perfect. Modifying and differentiating instruction will always need to occur for students to reach their optimal potential.

Unlock the Number Line

Image by:  Tratong

It’s becoming more evident that the Common Core initiative is running at full throttle. Keeping that in mind, I’m now finding myself exploring different methods to introduce fundamental math concepts and create lessons that emphasize number sense skills. These number sense skills are especially needed at a young age and often influence how students perceive / achieve in math later in their academic career.

Having students explain their mathematical thinking is a big focus next school year.  By asking appropriate questions, teachers are able to analyze and give feedback in real-time to best meet the academic needs of each student.  After researching math strategies and participating in a variety of CCSS workshops this summer, I’ve concluded (at least partially) that the number line can be utilized for many math objectives at the elementary level.

Teachers that model the mathematical problem-solving process find that it’s beneficial. The visualization of a numer line can be useful, whether it involves the concepts of measurement (elapsed time), percents (finding discounts), algebra (inequalities) or fractions (computation).  A number line can be useful in solving problems related to any of the above concepts.  If the idea of utilizing a number line to solve math is introduced via classroom instruction, it may be beneficial to give examples of how it’s used outside school as well.

So.. how did you use a number line today?

Building Student Rapport

Image by:  Keerati

Building rapport is essential in any organization.  In a school setting, developing student/teacher and parent/teacher rapport  can lead to increased learning.  Developing a positive relationship takes time and is often not discussed in teacher preparation courses.  Like many teachers find out, this topic is often part of the ‘on-the-job’ experience and evident during the first year of teaching.

To be an effective teacher, students need to understand that everyone at the school is there to support their learning.  Building student rapport is vital and that positive relationship often encourages students to learn at optimal levels.  Having stellar rapport can lead to increased student confidence.  Increased student confidence may lead to increased achievement. How do you build appropriate student/teacher rapport?  The list below isn’t all-encompassing, but I’ve used and found success with many of the ideas below. I’ve included a link in each line for more information.

What are some activities or strategies that you use to improve rapport?

Math Shortcut or Conceptual Understanding?

Image by:  Renjith

There are “tricks” or “shortcut” techniques that many teachers have in their tool belt when it comes to teaching mathematics.  These techniques are often memorized by students to be used later on some type of assignment.  I’m not saying that these types of techniques are good or bad, but often students come away with little conceptual mathematical understanding of the concept being taught via the shortcut. Click on the picture below for more information on conceptual understanding.

© 2007 – 2012 Regents of the University of California

Without that understanding, students are not necessarily being prepared to apply the concepts later in middle school/high school.  A very small sample of the short cut techniques I’m referring to are below.

PEMDAS – order of operations

King Henry Died Drinking Chocolate Milk – Metric System

FOIL Method – Algebra

Negative Multiplied by a Negative = Positive

Gallon Guy/Gal = Capacity

Students generally remember the shortcuts and utilize them on assignments/tests.  Is that a bad thing?  I can almost hear math teachers around the world grumble.   If the students truly have a conceptual understanding of the concept then why not use these techniques?  Many of these types of shortcuts are used at the late elementary level. When students understand the technique – such as King Henry .. but don’t understand the concept (differences between the units of measurement and in what context they can be applied) then students/teachers run into problems.  Students are expected to be able to apply the concepts in multiple situations. Middle school teachers are then are held responsible to deepen the mathematical understanding of the concepts behind the techniques that were briefly utilized at the elementary level.  This topic has been on my mind lately, and finally made it’s way into this post based on this post.  Elementary teachers, as most teachers do,  attempt to use innovative and engaging methods to produce excitement related to learning and school. That motivation is often contagious and beneficial.  Whether teachers use these techniques or not (obviously, it’s up to you!) students should understand the concepts before memorizing nifty sayings that don’t really relate to the concept itself.  I’m not blaming teachers for using these techniques to engage students, but ensuring that students have a mastery of the concepts should be near the top of the priority list.

Student Data – Beyond the Scores

Image by:  Adamr

At times, I think that the term “data” produces negative feelings from some educators.  Why?  Well … sometimes  the term is negatively associated with teacher accountability.  It’s also one of those buzz words that seems overused at times.   As an educator, information/data can be an important tool in my tool belt as I utilize it to inform and individualize instruction.  I’m surprised to find that the general public seems to view student data as just scores from standardized tests.  I don’t think that data can be limited to standardized assessment results.

Below,  I’m going to create a data collection list for educators.  I’m not going to include yearly state assessment data, such as MSA in my list.  I’ve found that standardized tests that are given once a year give little to no direction in informing instruction.  I remember a colleague once categorizing state assessments as autopsy reports.   They may be helpful in analyzing school data for school improvement goals, but for the individual teacher, they seem less than stellar.

Data Collection Tools –>

Survey Results – Collecting survey data can be one way to get to know your students on a personal level.  Developing rapport with students is key in helping them reach their potential.

Technology – Students can use iPads or computer activities to work on skills that need strengthening.  In the past I’ve used SplashMath to individualize instruction for specific students. For example, a student might receive only problems associated with place value for a certain time period.  I will get a report on a weekly basis on which problems were missed or correct.  This data can be emailed and utilized to inform further instruction. This feedback can immediately be put to good use.

Guided Groups – Guided math/reading groups can be a great way to collect data on individual students.  I’ve seen teachers travel around the room with a clipboard and collect student data in that manner.

Projects – Student projects can be utilized to collect student data.  Student work samples can also be used to develop a portfolio for each student.  Using a camera, educators can also take digital pictures to review and use during parent teacher conferences.

Journaling – Students write in journals about their skills and overall performance in the classroom.  I believe journals can be used in all classes.  I’ve had success utilizing journals in math classes.  When appropriate questions are asked, teachers can glean data regarding feelings about particular concepts that need revisiting.

Collaborative Work – Students often show dynamic strengths when working with a partner or group.  This type of information can be documented by the educator.  A self-reflection piece may also be helpful.

Unit Assessments – Unit assessments are not only meant to be graded and recorded.  Unit assessments can also be analyzed by students.  Students can check what questions were missed and set goals for their learning.

Exit Cards – Exit cards are generally given at the end of a lesson.  These cards are quick and informative.  Teachers can collect the exit cards and even have the students analyze the results.  Students can determine strengths/concerns and document them in a journal.

Student Data Binders – Students can place homework, tests, and projects in an individual data binder.  This binder should be a transparent way for teachers, parents, and students to review data to view strengths/concerns.

Standardized Assessment Data – The type of data that I’m talking about for this category relates to assessments that are given more than once per year.  An example could be the NWEA MAP assessment.  This assessment data can be used to find strengths/concerns and individualize instruction for students.

Math Reasoning and Feedback

Image by:   J. Creationz

Having math reasoning skills is important.  Generally, math reasoning skills are taught and incorporated in early elementary school.  In math, a problem is what a student is asked and expected to answer.  If a student is unable to answer why their answer is correct, I believe that the student might not fully grasp the mathematical concept.  The student might not be utilizing math reasoning skills.

For example, a student that measures area in linear feet might not completely have an understanding that area is measured in square units.  The student could have the correct numerical answer, but include the wrong unit (centimeters compared to square centimeters).

How is mathematical reasoning taught?  I’m going to be taking a proactive step next year to give opportunities for my students to utilize math reasoning.  I’m deciding to use higher level questioning to enable students to think of the process in finding the solution.  The learning process is key.  I’ve found that math instruction isn’t always linear, just as mathematical reasoning isn’t rigid.  By asking students why/how they arrived at a solution is vital in understanding their thinking.

As I’m planning for next school year, I’ve decided to ask students to explain their reasoning more frequently.  By hearing their reasoning, I’m in a better position to give direct feedback.  All math questions have some type of reasoning.  I believe that multiple solution / open-ended questions can be used to display mathematical reasoning. Students need to be able to explain why they responded with a specific answer and what methods/connections were utilized to solve the problem.  Based on the math Common Core, students are expected to reason abstractly and quantitatively.  When students describe their mathematical process, teachers are better able to diagnose and assess a student’s current level of understanding.  Math reasoning isn’t always quantifiable, but it can be documented via journaling and other communication methods.  More importantly, teachers will be able to provide specific feedback to help a student understand concepts more clearly.  I also feel that this questioning process develops self-confidence in students and prepares them to become more responsible for their own learning.  See the chart below.

Problem –> Reasoning –> Feedback