Evaluating and Improving a Learning Trajectory for Linear Measurement in Elementary Grades 2 and 3: A Longitudinal Study

Clements, Douglas
Barrett, Jeffrey
Sarama, Julie
Cullen, Craig
McCool, Jenni
Witkowski-Rumsey, Chepina
Klanderman, David
Contact Info: 
Publication Type: 
Publication Date: 
In Press

We examined children’s development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching.We checked the hierarchical structure of the trajectory by generating formative instructional task loops with each student and examining the consistency between our predictions and students’ ways of reasoning. We found that attending to intervals as countable units was not an adequate instructional support for progress into the Consistent Length Measurer level; rather, students must integrate spaces, hash marks, and number labels on rulers all at once. The findings have implications for teaching measure-related topics, delineating a typical developmental transition from inconsistent to consistent counting strategies for length measuring. We present the revised trajectory and recommend steps to extend and validate the trajectory.

Social Media and Technologies Toolkit

Email contact: 
Education Development Center

It seems like there are new tech and social media tools coming out every day. So what’s out there? And how can these tools be used to enhance your work?

CADRE has compiled a toolkit of new and potentially useful tech tools, social media tips and so on. The CADRE Team will keep this page updated with any new tools that come our way, so stay posted! (see NEW! posts below)

Using something that you think is great? Email us at cadre@edc.org.


5 Useful Webtools You Don’t Know Exist
Collaborate real time on a document…get rid of YouTube ads and comments on videos that you want to show…chop a YouTube video to show that parts that interest you…schedule meetings easier…shorten multiple URLs into one. To learn more about these 5 tools, visit this site.

5 Cross-Platform Mobile Development Tools You Should Try
Building a mobile development tool and don’t know which platform to use? Mashable suggests 5 cross-platform options.

Mobile Learning Resources
If you are looking for educational mobile app suggestions for iPod Touch and/or iPad, this site is a good starting place.

6 Free Facebook Apps for Building Custom Tabs
Apps that make it easy to add functionality to your Facebook page so that it no longer looks like it came ‘straight out of the box’.

Top 10 Facebook Apps for Fan Engagement and Building Community
If you are looking for new and creative ways to engage Facebook fans, this list of 10 apps could be just what you are looking for.

Built for students by students, Hoot.Me is a Facebook application that allows you see what your classmates are working on and collaborate inside of Facebook.

What is Vine?
Vine is an app that enables users to create and post looping videos to Facebook or Twitter.

Education-specific Social Media Platforms:

With more than 34 million users, Edmodo offers a free and secure social learning network for teachers and students.

YouTube For Schools
This new YouTube channel allows you to access thousands of free high quality educational videos on YouTube in a controlled environment.

EdWeb is a professional social network for the education community that is designed to connect colleagues, create learning communities, share and collaborate, and mentor new teachers.

Discovery Education Network
This global community of educators of more than 100,000 members connects teachers both on-line and in-person. Discovery Educators have exclusive access to a wide range of resources, professional development activities, networking opportunities, exclusive Discovery Educator events and more.

SmarterCookie is an online video coaching platform to help teachers improve their practice in the classroom. It allows you to upload videos and share them privately so that whoever you share the video with can provide feedback.

Similar to SmarterCookie, Edthena allows you to upload recorded videos and receive feedback, with next step goals.

Social Media Tips:

Social Media Examiner
From tips to product reviews, social media examiner puts out new and useful social media information multiple times per week. If your project is using social media or thinking about branding, this site is definitely worth visiting.

The Social Conference Directory
Want to find out about obscure conferences? Lanyrd is a “wiki” of conferences happening around the world. You can add conferences you’re attending, see what conferences other people are attending or just browse conferences by topic.

The Social Networking Infographic
Wondering what social networks are on the rise? Check out this cool infographic. To see the most popular social networks by country, check out the World Map of Social Networks.

3 Tools for Improving Your Social Media Strategy
These free tools help you monitor your social media and find pertinent posts.

Social Media Analytic Tools
Monitor your social media activity by using one of these statistical tools.

What is Klout?
Klout measures this influence across several social networks and shows users how they impact the people connected to them.

50 Top Tools for Social Media Monitoring, Analytics, and Management
This is a comprehensive list of social media tools with a description of what each tool does best. Some of the tools are free; some cost money.

Storify is a great tool for capturing posts and tweets in a purposeful and digestible way. Example: This CADRE storify captures tweets from an NSF STEM Smart workshop on early childhood learning.

Pinterest: For Education & Technology
This Pinterest board features education and technology tips and resources.

Just Getting Started With Facebook/Twitter/YouTube/Google+/LinkedIn?:

Facebook Groups Vs Pages: The Definitive Guide
What is the difference between a Facebook Page and Group? See The Definitive Guide to find out. P.S. For an example of a Facebook page, you can visit the CADRE Facebook page.

How To Create A Facebook Page
There are many sites that are helpful when creating a Facebook page. We picked this one because a) it has screen grabs b) it seems up-to-date and c) if you continue to scroll down, you will also find some helpful tips for more advanced Facebook learners, such as how to change the url of your Facebook page.

Twitter to Facebook: 5 Ways to Post to Both
Don’t want to post something twice? Mashable talks about 5 potential options to link your Twitter page to Facebook.

Facebook To Twitter
If you’re more Facebook-focused for your project and want your Facebook posts to be tweeted, go to this site to set this up.

How To Set Up A YouTube Channel
In true YouTube fashion, this describes how to set up your own YouTube Channel…via video.

How To Get Started With Google+, Your Complete Guide
Whether you have already been invited to try out Google+ or just want to see what all the hype is about, this guide will walk you through some features of Google+, as well as offer tips on how to set up your profile, settings, and circles.

The Beginner's Guide to Tumblr
Tumblr is a micro-blogging platform that churns out millions of posts on a daily basis. Learn how to get started!

How to Build A Thriving LinkedIn Group
If you are considering starting a LinkedIn Group, here are some best practices.

Reddit: A Beginner's Guide
Reddit is essentially a message board. Like Twitter, the information is real-time, but unlike Twitter, the Reddit community votes on the content so that items of value or interest end up on the top.

Free Screencast/Webinar Options:

5 Free Tools For Creating a Screencast
Mashable has found 5 free screencast tools. Each tool works better for some things than others. Read more on Mashable.

Big Blue Button
Big Blue Button is an open source web conferencing option that has education in mind.

Facebook-Skype Video Calling: A Getting-Started Guide
A step-by-step guide on how to start using Skype via Facebook today. Skype offers face-to-face time and screensharing (free for one-on-one calls)

Skype in the Classroom
Skype offers a free and easy way to open up your classroom to experts and teachers from around the world. Not sure how to incorporate Skype into your classroom? Check out Edudemic’s article on “50 Powerful Ways To Use Skype in the Classroom”.

Google Hangout
This free platform can host up to 10 video feeds, allows screensharing, and even has some fun icebreaker features such as adding hats to your video feed!

This free platform can host up to 12 video feeds for a face-to-face virtual meeting (however, screensharing is an added feature that costs money).


Blogs About Technology And Education (some include great tips!):

History Tech
A former teacher, and present-day curriculum specialist at the Educational Service & Staff Development Association of Central Kansas, Glenn Wiebe writes about technology from an educational viewpoint.

EdTech Toolbox
Created as a place to share e-learning and Web 2.0 tools for education, this site has a regular blog, iPad apps, google tricks and more. Unfortunately, this blog was last updated in 2011, so some of the information may be outdated.

Top Rank Blog
The blogs on this site focus on marketing, as well as social media. The blogs include tips as well as opinions on current marketing and social media tactics.

The 50 Best Blogs for STEM Educators
A collection of blogs on Science, Technology, Engineering, Math and Education, recommended by BestCollegesOnline.com.


Publication Type: 
Publication Date: 
In Press

K-12 Resources for Science, Technology, Engineering and Mathematics Education A website collection of resources and findings generated through educational research and development projects funded in part by the National Science Foundation can help inform states and school systems that are developing strategies for improving K-12 STEM (science, technology, engineering and mathematics) education.

Doodle - Meeting Scheduler

The world’s leading online scheduling tool, Doodle takes the pain out of finding the right date and time for a group of people to meet and makes scheduling virtually effortless. The basic service is a free online coordination tool which requires neither registration nor software installation.

PhDs.org Jobs Database


PhDs.org was originally created with the help of a number of students while I was an assistant professor in the Math Department at Dartmouth College. The site was made possible by the generous support of the Alfred P. Sloan Foundation and a Burke Research Initiation Award from Dartmouth College. I have continued to run the site on my own since moving to Microsoft Research and subsequently to a consulting career.

The goal of the site is help students to prepare for the changing demands of today's job market and to provide a voice for early career scientists.

Common Misconceptions about Heat and Insulation

Fries-Gaither, Jessica
Publication Type: 
Publication Date: 
December 2009

The concepts of energy and heat are challenging for elementary students. Because young students are not ready to delve into kinetic theory and molecular motion, much of the explanation of heat and energy transfer is inaccessible to them. In addition, the use of the word "energy" in popular culture may interfere with the development of scientific understanding. Nevertheless, elementary students are capable of exploring heat through observations and qualitative, developmentally appropriate explanations. In fact, the idea that heat is transferred from one object to another via conduction is a grade-level expectation according to the National Science Education Standards (NRC 1996). During these initial explorations, teachers will encounter a variety of student misconceptions. Formative assessment and purposeful teaching will help prepare students to tackle more advanced concepts in the middle grades and beyond.

In this article, we've highlighted some common misconceptions about heat and insulation. Rather than provide an exhaustive list of all possible student ideas, we hope to give insight into ones that might be held by your elementary students. We've also provided tools for formative assessment and resources for teaching correct scientific concepts.

Syndicate content