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
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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

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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?

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

Just Getting Started?:

What's Really the Difference between Facebook Pages, Groups, and Profiles?
What is the difference between a Facebook Page, Profile and Group? See this article 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.

Getting Started with Twitter
Learn about the basics on this Twitter help page.

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

LinkedIn Groups 101
If you are considering starting a LinkedIn Group, here is how to get started. In addition, LinkedIn has created a 101 guide to building an engaged community.

Instagram is a popular visual social media tool. Watch this video on how to get started using Instagram.

Pinterest is a collecting and sharing social media tool. Learn more at about how to get started and use Pinterest.

In 2015, Snapchat was the fastest growing social network. See this article to learn how to use it to promote your work.

How To Get Started With Google+
Google help page on getting started with Google+.

How to Use Tumblr
Tumblr is a micro-blogging platform that churns out millions of posts on a daily basis. Learn how to get started!

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. See Reddit's beginner's guide and accompanying video.


How to Post from Twitter to Facebook
Don’t want to post something twice? This describes how to link your Twitter feed to your Facebook profile.

How to Post from 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 Create Custom Tabs for Your Facebook Page
Learn how to create custom tabs on your Facebook business or community page to showcase custom content alongside the default tabs (e.g. "About" and "Likes").

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

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.

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.

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:

This digital media website will keep you up to date on the latest happenings in social media.

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 2015 State of Social Media Infographic
Wondering what social networks are on the rise? Check out this 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.

19 Free Social Media Analytical Tools
Monitor your social media activity by using one of these analytical tools.

Recruiting Research Participants via Twitter (or Social Media)
This AEA365 blog gives tips on how to recruit research participants via Twitter and social media. The authors of the blog are researchers on the NSF-funded project, Twitter and Informal Science Learning and Engagement (TwISLE).

Free Screencast/Webinar Options:

The Best Screencasting Software for Teachers
This blog lists the pros and cons of different screencasting software options.

Big Blue Button
Big Blue Button is an open source web conferencing option that has education in mind. They just recently teamed up with Moodle.

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)

Microsoft Educator Community and Skype in the Classroom
Skype offers a free and easy way to open up your classroom to experts and teachers from around the world through the Microsoft Educator Community. 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!):

Edutopia STEM blogs
A collection of blogs on Science, Technology, Engineering, Math and Education.

We are Teachers Blog
The WeAreTeachers community engages teachers through social media. Their site includes blogs, resources and education directories.

The 50 Best Blogs for STEM Educators
This list was curated in 2011, but still has a number of active blogs that may be of interest.

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.

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.




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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
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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.

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