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Centre de recursos de referència per a l'ensenyament i aprenentatge de les matemàtiques a l'educació bàsica i batxillerat. Consulteu en especial els DOCUMENTS DE SUPORT i les CAMPANYES DEL CREAMAT. La quantitat d'activitats i propostes és enorme!

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El curs 2024/25 es posa en marxa el Programa Florence per la millora de la competència matemàtica de l’alumnat d’educació bàsica.
El programa s’adreça a 200 centres (120 de primària i 80 de secundària) que vulguin posar el focus en la millora de l’educació matemàtica… Llegeix més»

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Curriculum-linked resources for students aged 3-18, designed to nurture curious, resourceful and confident learners of school mathematics. All of our resources are free to use by teachers, students and parents. We are based in the Faculty of Mathematics at the University of Cambridge.

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search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Recull de problemes amb filtre per categories.

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Aquest web és un recull dels problemes realitzats per totes les associacions de docents de matemàtiques de Catalunya pel FEM MATEMÀTIQUES des de l’any 1993.

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Orientacions curriculars de matemàtiques de l’ESO

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Orientacions curriculars de matemàtiques de l’ESO

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Aquests documents d’orientació curricular pretenen donar suport als docents a l’hora de programar i a l’hora de dissenyar situacions d’aprenentatge i activitats d’avaluació. En tenir els sabers ben concretats, els docents poden planificar de manera més concreta i seqüenciada i poden adaptar les activitats d’aprenentatge a les necessitats de l’alumnat. A més, en incloure recursos i activitats, els documents poden ser molt útils com a modelatge de l’actuació a l’aula. Per altra banda, aquest desplegament també ha de permetre una millor coordinació i col·laboració entre els docents, ja que afavoreix una visió compartida i garanteix una major coherència pedagògica.

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Els problemes del Fem Matemàtiques poden ser un bon recurs pel professorat de matemàtiques com activitats competencialment riques.

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Banc de recursos de problemes competencials del concurs Fem Matemàtiques. Solucionari amb exemples d’alumnes i orientacions per al professor.

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Orientacions curriculars de matemàtiques de primària

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Orientacions curriculars de matemàtiques de primària

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Aquests documents d’orientació curricular pretenen donar suport als docents a l’hora de programar i a l’hora de dissenyar situacions d’aprenentatge i activitats d’avaluació. En tenir els sabers ben concretats, els docents poden planificar de manera més concreta i seqüenciada i poden adaptar les activitats d’aprenentatge a les necessitats de l’alumnat. A més, en incloure recursos i activitats, els documents poden ser molt útils com a modelatge de l’actuació a l’aula. Per altra banda, aquest desplegament també ha de permetre una millor coordinació i col·laboració entre els docents, ja que afavoreix una visió compartida i garanteix una major coherència pedagògica.

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Guies didàctiques Florence per a secundària

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Guies didàctiques Florence per a secundària

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Guies didàctiques on es presenten activitats per treballar determinats conceptes a les aules de secundària, amb els materials i la conferència on s'explica.

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Ja està oberta la inscripció al cicle de conferències sobre les guies didàctiques on s'hi presenten activitats per treballar determinats conceptes a les aules de secundària. Les cinc conferències i la realització d'un qüestionari certifiquen 10 hores.

En qualsevol moment del curs sou a temps d'inscriure-us!

Per assistir a les presentacions, cliqueu sobre la miniatura de cada sessió. La gravació de la conferència la podeu trobar, també, clicant sobre la imatge.
Guies ja presentades i material relacionat:

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FORMACIÓ FINALITZADA. Ja està oberta la inscripció al cicle de conferències sobre les guies didàctiques on s'hi presenten activitats per treballar determinats conceptes a les aules de secundà...

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Guies didàctiques Florence per a primària

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Guies didàctiques Florence per a primària

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Guies didàctiques on es presenten activitats per treballar determinats conceptes a les aules de primària, amb els materials i la conferència on s'explica.

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Recull d’activitats per matemàtiques de primària, creades el primer any del Programa Florence, juntament amb el seu material, que han estat incloses al repositori ARC i compartides pel CREAMAT.

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Activitats d’aula del programa Activitats per a 3r i 4t de primària A cop d’ull CM1 Comptar a cop d’ull és una bona manera de millorar el sentit numèric. Als primers cu…

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Prova Cangur, Olimpíada Matemàtica, Copa Cangur, Problemes a l'Esprint i altres. Hi podreu trobar els problemes plantejats als diferents concursos.

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Concurs individual i en format presencial, amb l’objectiu que l’alumnat participi i dediqui una estona a divertir-se tot resolent els reptes plantejats.

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PuntMat és un espai d'informació i divulgació d'activitats, materials i reflexions entorn a l'ensenyament de les Matemàtiques a l'etapa obligatòria. Vol ser una eina útil al servei dels docents a l'hora de preparar la feina. (Ana Cerezo, Cecilia Calvo, David Barba)

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Es poden complementar aquestes preguntes amb altres del tipus: què passaria si canviem nombres consecutius per senars consecutius? què passaría si en els cercles de color taronja hi ha altres disposicions de signes de suma i resta? o com descriuries el patró que compleixen els resultats de les següents seqüències:

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En aquest bloc es publiquen problemes, recreacions, activitats i temes divulgatius sobre matemàtiques que puguin ser d'utilitat a les aules. (Joan Jareño)

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Blog del Calaix +ie Un espai per les recreacions i la divulgació matemàtica especialment adreçat a les aules.

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HelloLogic! neix com una resposta a les novetats de la LOMLOE en l'ensenyament de les matemàtiques, destacant especialment el sentit socioemocional i la resolució de problemes com a eixos centrals de l'aprenentatge matemàtic. A més, HelloLogic! vol també posar un accent especial en el procés de raonament i prova, la capacitat de construir arguments que provin que la resposta trobada és la solució a un problema i per què. Aquest projecte ofereix reptes accessibles per a primària i secundària, amb el propòsit d'enfortir les competències transversals, el pensament lateral i la motivació per les matemàtiques.

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Cambridge Mathematics is a distinctive, evidence-based organisation, aiming for global impact by reshaping the landscape of mathematics education. Through an innovative, research-focused approach, powered by the connectedness of mathematical ideas, we are designing a coherent curriculum-agnostic Framework and supporting resources. Cambridge Mathematics is committed to enhancing curricula, refining assessments, and enriching learning and teaching, by offering opportunities for every learner, from their earliest experiences, to engage meaningfully in mathematical activity. We are leading change in mathematics education and are collaborating with international expertise in pursuit of this aim.

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For teachers and practitioners

Cambridge Mathematics recognises the essential role that teachers and practitioners play in mathematics education and aims to offer resources designed to support teachers and practitioners as designers: of tasks, lessons, sequences of lessons, and curriculum pathways. In the following sections you will find resources that are currently available, and you are invited to explore, discover, share and enjoy!

1. Approximately every two months we bring you an Espresso - a small but intense draught of filtered research on mathematics education, expressly designed with teachers and practitioners in mind
Read more

2. CoffeePods are a new, differently accessible format of Espresso content which have been designed to quench your thirst in places that other research summaries can't reach!
Read more

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Cambridge Mathematics recognises the essential role that teachers and practitioners play in mathematics education and aims to offer resources designed to support teachers and practitioners as designers: of tasks, lessons, sequences of lessons, and curriculum pathways. In the following sections you will find resources that are currently available, and you are invited to explore, discover, share and enjoy!

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Welcome! Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. (Fawn Nguyen)

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Welcome! Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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The Mathematics Assessment Project aims to bring the Common Core State Standards (CCSSM) to life in a way that will help teachers and their students turn their aspirations for achieving them into classroom realities. The project materials exemplify CCSSM in explicit down-to-earth performance terms and were produced as part of a collaboration between the University of California, Berkeley and the Shell Center team at the University of Nottingham, with support from the Bill & Melinda Gates Foundation. The team works with the Silicon Valley Mathematics Initiative and school systems across the US and UK to develop improved assessment.

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Classroom Challenges are lessons that support teachers in formative assessment. There are 100 lessons in total, 20 at each grade from 6 to 8 and 40 for 'Career and College Readiness' at High School Grades 9 and above. Some lessons are focused on developing math concepts, others on solving non-routine problems.

The Brief Guide for teachers and administrators (PDF) is recommended reading before using these lessons for the first time.

Each lesson is downloadable as an all-in-one PDF to print out, and a supporting PowerPoint presentation.

Finding a Lesson

There are several ways of navigating:

1. Use the menu on the left to browse by grade and topic area, or search for a key phrase.

2. Go to the Standards tab to find lessons linked to a particular content standard or practice.

3. The complete set of lessons is listed below in alphabetic order.

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Classroom Challenges are lessons that support teachers in formative assessment. There are 100 lessons in total, 20 at each grade from 6 to 8 and 40 for 'Career and College Readiness' at High School Grades 9 and above.

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El Marro de nou, com les Matemàtiques, els jocs i l'educació, és conegut des de fa centenars, per no dir milers d'anys, en les cultures de tot el món. Volem que això continuí: jugar, pensar i educar-nos. (Lluís Mora)

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El Marro de nou, com les Matemàtiques,els jocs i l'educació, és conegut des de fa centenars, per no dir milers d'anys, en les cultures de tot el món. Volem que això continuí: jugar, pensar i educar-nos.

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Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM). Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.

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Illuminations Home - National Council of Teachers of Mathematics

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Youcubed is a research center at Stanford University’s Graduate School of Education, co-founded in 2013 by Professor Jo Boaler and Cathy Williams. We conduct research, design curriculum, and develop professional learning offerings centered around creative mindset mathematics. Our work transforms insights from research in neuroscience and mathematics education into practical classroom resources that help students experience math as accessible, visual, and beautiful.

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This exciting project partnership with George Mason University and the Virginia Department of Education (VDOE) is to offer strength-based formative assessment and bridging activities to support instruction for K-8 students. We wanted to tap into the geniuses in our school districts in Virginia and invited these amazing teacher designers to codesign these modules. They spent their summer designing these bridging activities and refined the modules by piloting them in their classrooms. We have strength in numbers as teacher designers supporting strength-based instruction for our students!

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Formative Assessment is an invaluable tool for supporting ongoing learning! Formative assessment (FA) is focused on identifying and understanding what and how students are thinking to provide feedback and/or adjust instruction to better meet students' learning needs (Black & Wiliam, 2009). The use of research based big ideas aligned to the learning trajectories research allows teachers to use frequent interactive assessments of students' learning to "make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have taken in the absence of the evidence that was elicited" (Black & Wiliam, 2009, p. 6)

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This exciting project partnership with George Mason University and the Virginia Department of Education (VDOE) is to offer strength-based formative assessment and bridging activities to support instruction for K-8 students. Standards are considered a bridge when they: function as a bridge to which

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Eines i materials de GeoGebra Ensenya i aprèn matemàtiques d'una manera més dinàmica GeoGebra és més que un conjunt d'eines gratuïtes per fer matemàtiques. És una plataforma per connectar professors i estudiants entusiastes i oferir-los una nova manera d'explorar i aprendre les matemàtiques.

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GeoGebra - the world's favorite, free math tools used by over 100 million students and teachers

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Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more

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Unleash your creativity with the world’s best virtual manipulatives!  Our mathematical playground is filled with unique tools that allow students to play and explore – and they’re completely free to use.

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Simulaciones interactivas de ciencias y matemáticas. Recursos para docentes, actividades, y comunidad Los maestros tienen acceso a consejos específicos sobre simulaciones, incluyendo videos, recursos para enseñar con simulaciones y actividades compartidas por nuestra comunidad de maestros. University of Colorado Boulder.

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Fundado en 2002 por el ganador del Premio Nobel Carl Wieman, el proyecto de simulaciones interactivas de PhET de la Universidad de Colorado en Boulder crea simulaciones interactivas gratuitas de matemáticas y ciencias. Las simulaciones de PhET se basan en investigación educativa extensiva e involucran a los estudiantes mediante un ambiente intuitivo y similar a un juego, en donde aprenden explorando y descubriendo.

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We believe that learning mathematics can and should inspire joy. The Global Math Project is a worldwide movement of teachers committed to igniting and sustaining a love of mathematics in their students. It all starts with James Tanton’s Exploding Dots.

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Tens of thousands of teachers have used our exemplar curriculum to bring math joy to over 7 million students across the planet. Transform how students perceive mathematics!

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Aquest web pretén ser un lloc on trobar informació sobre la història del desenvolupament de les numeracions orals i escrites. També un espai on trobar propostes d’activitats d’aula sobre aquest tema. (Joan Jareño)

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Aquesta pàgina no fa servir marc i no la pots visualitzar correctament

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Bringing Ideas to Life

13,000+ Interactive Wolfram Notebooks for education, research, recreation and more

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Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

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FREE mathematical activities, puzzles, problems, visual aids, investigations and lots more. Enter Transum Maths to see how teaching and learning this fascinating subject can be fun.

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A large collection of free interactive online activity supporting the teaching and learning of Mathematics.

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The “Slow Reveal Graph” instructional routine promotes cross-curricular sensemaking about data. As more and more of the graph is revealed, students refine their interpretation and construct meaning, often in surprising ways. SlowRevealGraphs.com is curated by Jenna Laib, a K-8 math specialist near Boston, MA (USA).

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Slow Reveal Graph is an instructional routine that promotes sensemaking about data. This highly engaging routine uses scaffolded visuals and discourse to help students (in K-12 and beyond) make sense of data. As more and more of the graph is revealed, students refine their interpretation and construct meaning, often in surprising ways.

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El Gabinet de Materials i de Recerca per a la Matemàtica a l’Escola (GAMAR) està vinculat a la Càtedra de Didàctica de les Matemàtiques Maria Antònia Canals que va ser creada el juliol del 2021, gràcies a un conveni conjunt de la Universitat de Girona, el Departament d’Educació i l’Ajuntament de Girona.

L’objectiu principal de la Càtedra és impulsar el desenvolupament professional dels mestres i contribuir fermament al desenvolupament de la competència matemàtica dels nens i nenes.

En aquest espai es poden trobar propostes per treballar amb materials ordenades per temàtica i edat.

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GAMAR - GAMAR. Gabinet de Materials i de Recerca per la Matemàtica a l'Escola

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Este portal es de la "Red Educativa Digital Descartes" (RED Descartes), asociación no gubernamental sin ánimo de lucro constituida el 1 de junio de 2013 que tiene como fin promover la renovación y cambio metodológico en los procesos de aprendizaje y enseñanza de las Matemáticas, y también en otras áreas de conocimiento, utilizando los recursos digitales interactivos generados en el Proyecto Descartes. En particular, para la consecución de este fin, se promueve el desarrollo y difusión de la herramienta de autor denominada "Descartes".

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Utilizamos cookies para mejorar nuestro sitio web y su experiencia al usarlo. Las cookies utilizadas para el funcionamiento esencial de este sitio ya se han establecido. Para saber más sobre las cookies que utilizamos y cómo eliminarlas , consulte nuestra Política de Privacidad.

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Utilizamos cookies para mejorar nuestro sitio web y su experiencia al usarlo. Las cookies utilizadas para el funcionamiento esencial de este sitio ya se han establecido. Para saber más sobre las cookies que utilizamos y cómo eliminarlas , consulte nuestra Política de Privacidad.

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Desmos Studio is a Public Benefit Corporation with a goal of helping everyone learn math, love math, and grow with math.

Our free suite of math tools, including our Graphing Calculator, is used annually by over 75 million people around the world. Those tools help people represent their ideas mathematically, connect different representations dynamically, make conjectures, and then develop entirely new ideas. They also result in some pretty spectacular art.

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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Revista adreçada a docents de matemàtiques.

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Dues entitats molt representatives dels professionals de la docència de la matemàtica catalana, com són la FEEMCAT -que aplega principalment mestres i

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Publicacions del Museu de Matemàtiques de Catalunya

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Publicacions - Museu de Matemàtiques de Catalunya

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A través de la resolución de problemas 🔸 Probabilidad y estadística 🔸 Números naturales 🔸 Medida y racional 🔸 Enteros y álgebra 🔸 Geometría 🔸 Funciones 🔸 Didáctica de las matemáticas 🔸 Educación en general

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Gran parte de lo que escribo viene de mi cuenta de Twitter, cosa que indico en las entradas correspondientes de este blog. Escribir en dicha red social implica asumir el límite de 280 caracteres, lo cual obliga a encadenar varios tweets en lo que se conoce como hilos, resultando en una forma especial de redactar.

Siempre que escribo sobre alguna propuesta didáctica para un contenido en concreto (probabilidad, naturales, etc.) es a través de la resolución de problemas. Con la idea de facilitar la navegación por aquí la categoría A través de la resolución de problemas estará dedicada a aspectos generales. Lo mismo ocurre con la categoría Didáctica de las matemáticas.

¡¡Sistema de categorías EN CONSTRUCCIÓN!! La idea es replicar lo de mi tweet fijado. Paciencia 🙏.

A través de la resolución de problemas 🔸 Probabilidad y estadística 🔸 Números naturales 🔸 Medida y racional 🔸 Enteros y álgebra 🔸 Geometría 🔸 Funciones 🔸 Didáctica de las matemáticas 🔸 Educación en general

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Profesor Titular de Didáctica de las Matemáticas

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The Shell Centre for Mathematical Education is known around the world for its innovative work on mathematics education. This site offers freely downloadable versions of a range of the Centre's out-of-print publications - including the seminal Language of Functions and Graphs along with many other books and research papers.

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Shell Centre for Mathematical Education Publications Ltd.

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Shell Centre Publications Ltd. was set up to distribute and license materials developed at the Centre, and offers a range of innovative teaching materials for mathematics education, together with research publications and tests from the Centre and its collaborators.

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Qui és l'intrús?

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© site Copyright 2024 Talking Math with Your Kids • Saint Paul, MN, 55114 Rights to individual sets controlled by the named authors

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Finkel and Katherine Cook.

We develop math games and curriculum, including tons of free lesson plans that we give away here. And we write puzzles, produce math-art shows, and do whatever we can to show people how playful, beautiful, and life-changing mathematics can be.

Openers, games, rich tasks.

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An index of some of our favorite lessons. We recommend starting with openers or games if this is your first time here.

Want more?
The Math for Love curriculum offers enough supplementary lessons to enrich the entire school year, or teach a month-long summer program.

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An index of some of our favorite lessons. We recommend starting with openers or games if this is your first time here. Want more? The Math for Love curriculum offers enough supplementary lessons to enrich the entire school year, or teach a month-long summer program.

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Rich resources for teaching A level mathematics

Enabling all students to explore the connections that underpin mathematics

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Overview

Our resources are organised into topics or stations on a map or tubemap showing the connections between them.

Watch this video or use the preceding menu to find out more.

The map

The mathematics has been organised along a system of tube lines, which reflect big themes that run through mathematics. The tubemap offers a way to navigate to resources for teaching a particular area of mathematics; resources can be accessed by clicking on a station name. Some stations are still in development and this is indicated by a construction symbol.

You can access the map at any time by clicking the Map button in the main menu.

Stations

Each station features an overarching question that could be used to stimulate curiosity. There are a number of key questions that summarise the ideas that arise in the resources. You can filter resources by selecting a key question. You can also filter resources by tube line, if you wish to choose a resource with a particular emphasis.

The resources that are available at each station may come under three headings. Resources that introduce new ideas relating to the station are in the "Introducing" section. "Developing" resources may build on these ideas or earlier work. "Review questions" are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking.

Resources

To help you find the resources you are looking for, we have classified them according to twelve resource types.

Resources are divided into sections. In some cases this may be a warm-up followed by a larger task, and others may have a problem followed by a suggestion of how to tackle it. Almost all resources contain a solution or a "Things you might have noticed" section. This may help you to think about questions you might ask students, to see areas where students could get stuck, or offer further insight into how you might use the resource in your classroom. Further support is offered in the teacher notes.

Pervasive ideas

By clicking on a pervasive idea you will find a description of how the idea arises within the resources. If pervasive ideas are highlighted in a resource they appear in the sidebar (or bottom-bar on a small screen) and in the list of resources at the station (on a wide screen).
What are pervasive ideas?
Search

Use the Search button in the top menu bar to open the search dialog.

You can search for resources by title, keywords or text within the resource. Review questions can be searched by question Ref. You can also search for pervasive ideas and mathematical processes such as visualising.

You can also browse all our material with filtering options by clicking the Browse button in the main menu.

Saving resources

You can save a resource for later by adding it to your resource collection. To do this click the star next to the resource title. Note you must log in or register to use this facility. To access your resource collection, click the User button in the top menu bar then Your resource collection.

Within your resource collection, you can organise your resources by creating ordered subcollections. To add a resource to a subcollection, click the add to subcollection icon in your resource collection table. To select a subcollection, use the drop-down list above the table. You can also generate a PDF of resources from a subcollection, which could be used to generate your own exam from our review questions, for example.

Bundles and more

The More menu in the top right contains links to the Underground hub, our About and contact page and the Your mathematical classroom section of the site.

Our About page contains a video explaining our philosophy.

The Your mathematical classroom area of the site is accessible from the More menu and has been coloured purple to distinguish it from the rest of the site, as well as having its own menu once inside this area. It contains support for using our resources in the classroom as well as professional development opportunities. This includes the Bundles page, which contains small collections of resources that have a particular focus or goal, our Resources in action page, which provides detailed teacher support for a handful of resources, our blog, upcoming and recorded webinars, a courses page, and information about our Champions programme.

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A level maths teaching resources | Underground Mathematics

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Rich resources for teaching A level maths, enabling all students to explore the connections that underpin mathematics. The resources are free for all users.

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Banc d'activitats de matemàtiques

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CS Unplugged is a collection of free teaching material that teaches Computer Science through engaging games and puzzles that use cards, string, crayons and lots of running around.

Hi ha versió en castellà.

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CS Unplugged is a collection of free teaching material that teaches Computer Science through engaging games and puzzles that use cards, string, crayons and lots of running around.

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Math Problem Database to make math classes a little more enjoyable for students worldwide.

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Dan Meyer 3 Acts Real World Math Tasks | Perplexing Questions by Dan Meyer

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3 Acts of a Mathematical Story: Real World Math Tasks by Dan Meyer. Perplexing Mathematics Questions Created By Dan Meyer.

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Activitats matemàtiques

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a ppt is here

an effort to collect together proofs that involve some form of geometrical insight

thanks to Dietmar Kuchemann

there are several good sources for geometrical problems
those by Ed Southall and Vincent Pantolini
and Catriona Shearer
are fairly well known

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a ppt is here an effort to collect together proofs that involve some form of geometrical insight thanks to Dietmar Kuchemann there are several good sources for geometrical problems those by Ed Southall and Vincent Pantolini and Catriona Shearer are fairly well known

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Policubos para una “polimatemática” en el aula

Autores:

Ángel Alsina (Cátedra de Didáctica de las Matemáticas M. Antònia Canals. Universitat de Girona. España)

Ester Bosch i Casas (Gabinet de Materials i de Recerca per a la Matemàtica a l’Escola, GAMAR. España)

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Reptes matemàtics i altres continguts de Paulo Ferro.

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Idees centrals de matemàtiques infantil i primària

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Idees centrals de matemàtiques infantil i primària

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QUÈ ÉS UNA IDEA CENTRAL?

Idea que és fonamental per a l'aprenentatge de les matemàtiques i que vincula nombrosos aprenentatges matemàtics de manera coherent.

Burgués, C. i Serra, T. (2019)

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LES IDEES CENTRALS DE MATEMÀTIQUES A L'EDUCACIÓ PRIMÀRIA El desenvolupament de la competència matemàtica, entesa com la capacitat de raonar matemàticament i d'utilitzar conceptes, procediments, fets i eines per descriure, explicar i predir fenòmens (Departament d'Ensenyament, 2012), comporta que

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CHALLENGING MATH PROBLEMS WORTH SOLVING

The name “Open Middle” might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:

a “closed beginning” meaning that they all start with the same initial problem.

a “closed end” meaning that they all end with the same answer.

an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.

Open Middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking.

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Activitats geogebra

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I am the [color=#1551b5]Mathematics Coordinator[/color] for [color=#c51414]Merced County Office of Education[/color]. I mostly work with teachers in ...

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El origen de la escritura de los números

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El origen de la escritura de los números

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Article de Cultura Científica

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El origen de la escritura de los números — Cuaderno de Cultura Científica

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El estudio de la historia de la humanidad se divide en dos grandes períodos, que son la prehistoria, que abarca desde la aparición de la especie humana, desde sus primeros ancestros, hasta la aparición de la escritura, y la historia, que abarca desde el final de la prehistoria hasta la actualidad. Se considera que el […]

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Bloc de la matèria de matemàtiques de l'INS Baix a Mar de Vilanova i la Geltrú

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Bloc de la matèria de matemàtiques de l’INS Baix a Mar de Vilanova i la Geltrú

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Orientacions pràctiques per a la millora de la geometria

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Orientacions pràctiques per a la millora de la geometria

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El propòsit de les presents orientacions pràctiques és contribuir a aquest esforç que ha de fer possible la millora del coneixement i les habilitats.

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Blog de Antonio Omatos

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MatemaTICzando la realidad – Aprender matemáticas de forma diferente

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Activitats geogebra

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Blog de Manel Martínez i Jordi Campos

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Blog amb activitats i recursos

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Web amb algunes lliçons i recursos gratuïts.

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I train mathematics educators who want their students to be better problem solvers.

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Dossiers del departament de Matemàtiques INS El Sui amb llicència Creative Commons

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Recursos i experiències

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MÒDUL 1 Què en sabem d'allò que s'anuncia com a objectius a aconseguir en aquest curs? Què esperem del curs? Què coneixem dels conceptes claus com Entorn Personal...

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MathPickle is a practical site for teachers. Here, you will find curricular puzzles and games that simultaneously engage your gifted and struggling students. This will help with classroom management!

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I stumbled upon your site, MathPickle.com, this morning and two hours later I'm still there. Just wanted to drop you a brief note to say thank you for all the great resources, ideas, and inspiring videos! I can't wait to use some these materials this Fall with my elementary mathematics methods students as well as try the unsolved problems with my two children. Amy Tanner

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I stumbled upon your site, MathPickle.com, this morning and two hours later I'm still there. Just wanted to drop you a brief note to say thank you for all the great resources, ideas, and inspiring videos! I can't wait to use some these materials this Fall with my elementary mathematics methods students as well as try the unsolved problems with my two children.

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Materials del programa PCMAT, de millora la competència matemàtica de l’alumnat de primària a través del pensament computacional, la programació i la robòtica educativa.

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Computational Thinking is often mistakenly equated either to computer technology/digital literacy or to programming. CT has a much wider scope. So what exactly is computational thinking? We define CT as a skill that promotes a unique way of thinking about problems, that uses the power of logic, algorithm, abstraction, and precision.

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Trencaclosques, reptes, problemes, un llistat amb què fa especial cada nombre i una taula periòdica amb matemàtics destacats al llarg de la història.

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This site is written by Rachel Lambert, a former classroom teacher, special education teacher, and currently an associate professor in the Gervitz Graduate School of Education at University of California Santa Barbara.

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On Saturday, 11/5/16 I did a presentation at PME-NA in Tucson about a research review I recently did on increasing the participation of students with LD in mathematical problem solving and discussion.

The basic idea is this: why is intervention in mathematics always focused on content. Could we also design intervention in participation?

When a learner is having difficulty in class, we assess that learner. We try to figure out what the learner knows, and what they don't know. This is an assumption, however, about mathematical knowledge: that it exists independently in the brain, and those who know can recall it without assistance. It also assumes that we are focused on the content standards, rather than the practice standards. While understanding knowledge as individual, as memorized, is important for certain aspects of mathematics, it is not all of mathematics. Secondly, focusing on content as the basis of intervention focuses on the individual as the problem. But what about the classroom? Why didn't the student "get it" the first time? Yes, we can "reteach" but perhaps we ought to take a closer look at what is happening in the classroom to make this content accessible, or not, to all learners.

In general, students with disabilities have less access to standards-based mathematics, since they all too often segregated from the general education population into self-contained classrooms. These separate classrooms tend to focus on more procedural mathematics (Jackson & Neel, 2006) and more basic content (Kurz et al., 2010).

In an article I wrote with Trisha Sugita, we looked at some studies of the engagement of students with learning disabilities (referring to specific learning disabilities, which includes dyslexia and dyscalculia) when these students are included in standards-based mathematics. In a study of the participation of students in a standards-based mathematics curriculum, students with LD did not participate in whole group mathematics discussion, and tended to focus on non-mathematical tasks such as materials management during small group work (Baxter, Olsen & Woodward, 2001). In another study, students with LD were called on fewer times than other students, and were less involved in small group work (Bottge, Heinrichs, Mehta, & Hung, 2002).

These studies suggest that just including kids with LD in standards-based mathematics is not enough. We need to deepen engagement and participation for these students. We found a small number of studies (n=7) that looked at the participation of students with LD in standards-based mathematics and found that particular teacher moves appeared to increase engagement and participation.

The design of curriculum may be critical. Students were supported in standards-based mathematics classrooms in which they were presented with tasks that offered multiple solution paths (Bottge et al., 2007; Foote & Lambert, 2011; Moscardini 2010). Students were supported by curriculum that was responsive to student thinking, so that teachers designed the tasks based not on a predesigned sequence but on the current understandings of their students (Carpenter et al., 1999/2014). Students were supported when mathematics curriculum provided multi-modal representations of content, and multiple ways of engaging in mathematical activity (Baxter et al., 2005; Bottge et al., 2007; Foote & Lambert, 2011).

These studies also suggested that teacher moves are critical in increasing student participation. While some studies documented significant differences in participation between students with LD and those who were not (Baxter et al., 2001; Bottge et al., 2002), there were classrooms in which participation was equalized (Foote & Lambert, 2011). In these classrooms, teachers supported student problem solving through strategies such as supporting student participation in discussion. Other strategies included rewording problems during problem-solving (Moscardini 2010) and supporting equity in small group work (Bottge et al., 2007). Teachers supported the equal participation of students with LD by giving equal status to presentations that included the notebook and manipulatives as supports (Foote & Lambert, 2011). Researchers noted that consistency in classroom routines may have increased the participation of students with LD.

Research in the mathematical learning of students with learning disabilities must focus attention on intervention in participation. This review included only a small number of studies that suggest a future direction for research in this area. Such research could provide a much needed focus on what learners who are labeled LD can do within standards-based mathematics, rather than what they cannot do. With increasing evidence that such students can construct effective strategies on their own (e.g. Peltenburg, Heuvel-Panhuizen, & Robitzsch, 2012), educators can no longer assume that standards-based mathematics will not work for these students based on perceived deficits. Nor can we assume that simply including students with learning disabilities in standards-based mathematics classrooms will lead to higher achievement. Instead, we must learn more about how to support all learners for full participation in standards- based mathematics classrooms. These supports are likely to be helpful for a wide range of learners, assisting teachers in making standards-based mathematics more equitable for all.

My favorite slide is this:

I thoroughly enjoyed reading this post by Anna Blinstein (@ablinstein) about a challenging class she is teaching. I love a post that begins with a real challenge, a problem that needs to be solved. She writes about a high school class that includes multiple grades, skill levels, and previous experiences with math. While typically successful in focusing her classroom around collaborative group work (using Thinking Classrooms), this class challenges her. She notices that the kids are disengaging from group work, and hears complaints that the class is moving both too fast and too slow.

Anyone who has taught has faced this challenge. This challenge is particularly common when we teach based on lectures, but that is not the case here- Anna has designed her classroom around best practices of group work and rich tasks. Other classes are working with a range of learners, but this one is not. While she is not writing specifically about students with disabilities, this post is a test case of the "good teaching is good teaching" myth. I believe that both "students need to be tracked, students with disabilities need different math" and "just put them together, good teaching is good teaching" belie how challenging it is to teach a wide range of learners.

So what does she do? According to this post, she does a tremendous amount, some of which is supported by already existing research, and some of which is innovative and should be researched. She writes

Some suggestions that I implemented that seemed to make a difference:

Taking a break from random groups to help students regain their trust that the class would meet their needs; doing some work in pairs designed to foster productive collaboration; allowing students choice as to who to work with while also asking them to work with different students at times; being explicit when the goal of a task was to build collaborative skills

I love that she writes here about trust, knowing that her job is to gain the trust of kids, not just in her as a teacher, but in her ability to organize a class that will work for them. She offers more options for engagement for kids in this class, individual, pair, and group, offering additional choice in whom they work with. She makes it clear that goals are not always content-focused. If this sounds a lot like UDL (Universal Design for Learning), you are right. She is building flexibility and choice into her classroom.

Structuring activities so there was time at the start for individual exploration before asking students to share their thinking with others thus giving more processing time for students who worked more slowly; circulating and helping some students get started; building more optional challenge into tasks for students who worked very quickly or who had already had prior experience with a topic; creating tasks that could be approached with a greater variety of methods and building more writing into tasks so that different ways of thinking mathematically could be valued

This paragraph is a master class in creating an inclusive classroom in math. Thinking time is super important, particularly as for many neurodiverse learners, processing time is perhaps the fundamental difference from their peers. If class rushes past them, they don't have the time to engage to their potential. Building in an optional challenge is a great way to engage students who don't need that time- I think we should spend more time talking about how to do that so that students who work faster are offered opportunities to think deeply, not just move on to the next topic. She writes about creating rich, multi-leveled tasks, and basically notes that she had to be more careful about the tasks being multi-leveled as her class was more heterogeneous in terms of skill level. She looks to her tasks, rather than to deficits in the kids, as a point of change.

Meeting students where they were to regain trust and buy-in; this included at times splitting the class into two groups (students chose which group to join) - a more free-form exploratory group with more open and challenging problems and a more structured group where students would get some problems to activate prior knowledge and smaller, more concrete problems that would build over time to greater generalization and abstraction and more teacher guidance and reassurance that they were on the right track

This is a great strategy, and very UDL, as it is focused on students making the choices about how they learn, rather than a teacher doing the categorizing and sorting into differentiation groups. I would love to hear more about how these groups worked, and how students responded to them. Also, did students always pick the same groups? Did it vary by topic?

Noticing struggling students' successes and highlighting them publicly; selecting which students would share their thinking to make sure that different voices could be heard over time

Here we see the important insights from Complex Instruction about status treatments, particularly important when working to establish status for kids with less status in heterogeneous environments.

Make sure to leave time for synthesis and practice problems (at different levels) during class - this helped address student concerns that they were leaving class with lots of questions and feeling unsettled about the concepts they had explored that day

Giving students more feedback during class about their understanding of a topic rather than relying more heavily on groupwork and self-assessment for students to know how they were doing and what might be helpful next steps

Here, she attends to making sure that students leave the class feeling secure in new knowledge. She attends to synthesis. Feedback is a critical element of learning, with kind of an unfortunate name that suggests a computational model of learning. But feedback is really getting human interaction around your work, to see what you think mirrored in another, and can be particularly important when coming from the teacher, since our kids (mostly!) value what we think about what they think. It makes our kids feel valued.

Providing more problems at different levels and helping students navigate which problems might be more helpful for them to do during/after a particular lesson - here is an example of a tiered homework problem set.

I love this example of a tiered homework problem set. It begins by laying out the essentials, then gives problems that are Important, Interesting, and Challenging. I love that these are not reducible to Easy, Medium and For The Smart Kids. The first set is Important, which is why you should do them.

This post helps us build on the important work of Complex Instruction, layering in practices that allow kids to learn in their Zone of Proximal Development, making choices about their own learning, which leads to increased meta-cognition.

Yes, as Anna notes, this is an unsustainable amount of work. Yes, this is a tremendous amount of work, but the structures that you put into place are repeatable. That lovely homework, for example, is now made! Can departments, can the #MTBOS share these kinds of differentiated assignments? UDL is meant to solve problems, and then to help save you work, to build flexible supports into classrooms as a key aspect of design, not afterthought.

And this post is a perfect example of UDL in action. Here, she views curriculum and pedagogy as the problem, not the kids. She takes up a problem-solving attitude, working to redesign the classroom around the edges. This classroom redesign is not about the mythical middle, but working to make the class work for those who are on the edges, both needing more time and less, etc. The redesign builds in choice and flexibility as the primary tool to accomplish that.

A couple of years ago, James Sheldon and Kai Rand started a Working Group at the Psychology of Mathematics Education North America conference. This group, now called Critical Perspectives on Disability and Mathematics, is made up of mathematics education scholars who work at the intersections of disability and equity. We seek to create new discussions about disability and mathematics, discussions that move beyond deficit discourses. One of our projects was a special issue, which was just published in Investigations in Mathematics Learning. This special issue brings together scholars from mathematics education and disability studies in education. We are so pleased with the range of scholarship in this special issue. Check out the editor's introduction here for a introduction to all the articles in special issue: Lambert, Tan, Hunt & Candela 2018

For over two years, I have had a word document on my computer entitled, "Myths in Teaching Mathematics for SwD." I kept adding bits of writing, particularly when I encountered another myth. Imagine my excitement when Jo Boaler sent out a call for a special issue of Education Sciences on Myths in Mathematics Education. I am so proud to have a paper in this issue, which is amazing and available for free online. (I particularly recommend this amazing piece on dyscalculia by my colleagues Katherine Lewis and Dylan Lane)

My paper: http://www.mdpi.com/2227-7102/8/2/72

I decided to focus the paper on students with Learning Disabilities (or specific learning disabilities in reading, writing or math, otherwise known as dyslexia, dysgraphia or dyscalculia). While I wanted to write about a wider range of disabilities, the best research evidence was on this group of learners. I also picked two myths to focus on:

1. Students with LD ONLY benefit from explicit or direct instruction.

2. Students with LD cannot create their own strategies in math, and cannot handle multiple strategies.

The first is a major myth that I hear all the time, and the second is a kind of a sub-myth. The assumption that students with LD cannot construct strategies is so pernicious that I decided to include it as a separate myth.

I structured the paper around two things: first a quote written about students with disabilities. This was published in a prominent special education journal in 1998:

"The premise that secondary students with LD will construct their own knowledge about important mathematical concepts, skills, and relationships, or that in the absence of specific instruction or prompting they will learn how or when to apply what they have learned, is indefensible, illogical, and unsupported by empirical investigations.".

(Jones, Wilson, & Bhojwani, 1998, p. 161)

This quote still shocks me. Having known, taught, been a friend to and a family member or so many people with various permutations of LD, the idea that such learners cannot "construct knowledge" is exceptionally bigoted and wrong. This particular article described constructivism as "ideology" rather than a valid approach to teaching math. In the paper, I try to describe why these myths are themselves "indefensible, illogical and unsupported." I do not ignore the strong empirical evidence from special education mathematics that students with LD can benefit from explicit instruction, but I present evidence that suggests inquiry instruction as also effective. We also need to consider why we teach mathematics- it is not just to make students into effective computers, but to help them develop life-long identities as mathematical thinkers and explorers. The myth emerges from the assumption that there exists sufficient evidence that inquiry mathematics is NOT effective for students with LD, or that explicit instruction is the only method that is evidence-based. As the National Mathematics Advisory Panel states, "it is important to note that there is no evidence supporting explicit instruction as the only mode of instruction for students [with LD]" (2008, p. 1229).

As I was writing this piece, I checked Twitter and found this tweet:

Thank you Abby. This tweet inspired me to keep writing, and keep poring through research. If you are more interested in understanding the research divide between math ed and special ed, I would check out another article I wrote with Paulo Tan in Education Sciences ( http://www.mdpi.com/2227-7102/7/2/51).

Questions:

1. What myths still need to be unpacked?

2. What kind of research would you like to see around students with disabilities and mathematics? What specific questions have emerged from your work?

After I made the list of academic papers, I realized I should do something similar for writings that are aimed at teachers that take a non-traditional point of view on disability and teaching mathematics. Updated May 2018. Please comment if you have items to add!

Behrend, J. L. (2003). Learning-disabled students make sense of mathematics. Teaching Children Mathematics, 9(5), 269-73.

Chick, C., Tierney, C., & Storeygard, J. (2007). Seeing Students' Knowledge of Fractions: Candace's Inclusive Classroom. Teaching Children Mathematics, 14(1), 52-57.

Fosnot, C. (2010). Models of Intervention in Mathematics: Reweaving the Tapestry. National Council of Teachers of Mathematics.

Lynch, S. D., Hunt, J. H., & Lewis, K. E. (2018). Productive Struggle for All: Differentiated Instruction. Mathematics Teaching in the Middle School, 23(4), 194-201.

Storeygard, J. (2009). My Kids Can: Making Math Accessible to All Learners, K-5 (Pap/DVD). Heinemann.

Storeygard, J. S. (2012). Count Me In! K-5: Including Learners With Special Needs in Mathematics Classrooms (1 edition). Thousand Oaks, Calif: Corwin.

Storeygard, J., & Tierney, C. (2005). Including all students in meaningful mathematics: the story of Darrell. Teaching Exceptional Children Plus, 1(3).

Tan, P. (2017). Advancing Inclusive Mathematics Education: Strategies and Resources for Effective IEP Practices. International Journal of Whole Schooling, 13(3), 28-38.

I created this list based on a request for a Ph.D. reading list for a student interested in critical and Disability Studies approaches to mathematics education. Figured I should share with more, as there are so many wonderful resources on this list. Updated May 2018. Please comment if you have recommendations to add!

Behrend, J. L. (2003). Learning-disabled students make sense of mathematics. Teaching Children Mathematics, 9(5), 269-73.

Borgioli, G. M. (2008). A critical examination of learning disabilities in mathematics; Applying the lens of abelism. Journal of Thought, 43(12), 131-147.

Bottge, B. A., Stephens, A. C., Rueda, E., LaRoque, P. T., & Grant, T. S. (2010). Anchoring Problem-Solving and Computation Instruction in Context-Rich Learning Environments. Exceptional Children, 76(4), 417-437.

Chick, C., Tierney, C., & Storeygard, J. (2007). Seeing Students' Knowledge of Fractions: Candace's Inclusive Classroom. Teaching Children Mathematics, 14(1), 52-57.

de Freitas, E., & Sinclair, N. (2016). The cognitive labour of mathematics dis/ability: Neurocognitive approaches to number sense. International Journal of Educational Research, 79, 222-230.

de Freitas, Elizabeth, & Sinclair, Natalie. (2014). Mathematics and the Body: Material Entanglements in the Classroom. Cambridge University Press.

Fernandes, S. H. A. A., & Healy, L. (2013). Multimodality and mathematical meaning-making: Blind students' interactions with Symmetry. International Journal for Research in Mathematics Education, 3(1), 36-55.

Fosnot, C. (2010). Models of Intervention in Mathematics: Reweaving the Tapestry. National Council of Teachers of Mathematics.

Healy, L., & Fernandes, S. H. A. A. (2011). The role of gestures in the mathematical practices of those who do not see with their eyes. Educational Studies in Mathematics, 77(2-3), 157-174.

Hunt, J. H., Tzur, R., & Westenskow, A. (2016). Evolution of unit fraction conceptions in two fifth-graders with a learning disability: An exploratory study. Mathematical Thinking and Learning, 18(3), 182-208.

Hunt, J. H., Westenskow, A., Silva, J., & Welch-Ptak, J. (2016). Levels of participatory conception of fractional quantity along a purposefully sequenced series of equal sharing tasks: Stu's trajectory. The Journal of Mathematical Behavior, 41, 45-67.

Jackson, H. G., & Neel, R. S. (2006). Observing mathematics: Do students with EBD have access to standards-based mathematics instruction? Education and Treatment of Children, 29(4), 593.

Lewis, K. E. (2017). Designing a Bridging Discourse: Re-Mediation of a Mathematical Learning Disability. Journal of the Learning Sciences. Retrieved from http://www.tandfonline.com/eprint/A5wfenur9ZCNTn4atCtD/full

Lewis, K. E. ., kelewis2@uw. ed., & Fisher, M. B. ., mfisher4@uw. ed. (2016). Taking stock of 40 years of research on mathematical learning disability: Methodological issues and future directions. Journal for Research in Mathematics Education, 47(4), 338-371.

Lynch, S. D., Hunt, J. H., & Lewis, K. E. (2018). Productive Struggle for All: Differentiated Instruction. Mathematics Teaching in the Middle School, 23(4), 194-201.

Magne, O. (2001). Literature on special educational needs in mathematics: a bibliography with some comments. Retrieved from https://dspace.mah.se/handle/2043/6043

Moscardini, L. (2013). Primary special school teachers' knowledge and beliefs about supporting learning in numeracy. Journal of Research in Special Educational Needs, v15 n1 p37- 47(n1), p37-47. https://doi.org/10.1111/1471-3802.12042

Peltenburg, M. (2012). Mathematical potential of special education students (Dissertation). Utrecht University.

Sheldon, J. (2013). Erasing Queer Subjects, Constructing Disabled Subjects: Towards a Queering of Mathematics Disabilities. Retrieved from https://eric.ed.gov/?id=ED560838

Sheldon, J. (2017). Problematizing Reflexivity, Validity, and Disclosure: Research by People with Disabilities About Disability. The Qualitative Report, 22(4), 984-1000.

Sheldon, J., & Rands, K. (2017). Whatever Will Be Will Be: Queering Disabled Subjects' Temporality. Philosophical Inquiry in Education, 24(4), 368-378.

Storeygard, J. (2009). My Kids Can: Making Math Accessible to All Learners, K-5 (Pap/DVD). Heinemann.

Storeygard, J. S. (2012). Count Me In! K-5: Including Learners With Special Needs in Mathematics Classrooms (1 edition). Thousand Oaks, Calif: Corwin.

Storeygard, J., & Tierney, C. (2005). Including all students in meaningful mathematics: the story of Darrell. Teaching Exceptional Children Plus, 1(3).

Tan, P. (2017a). Advancing Inclusive Mathematics Education: Strategies and Resources for Effective IEP Practices. International Journal of Whole Schooling, 13(3), 28-38.

Tan, P. (2017b). TOWARD INCLUSIVE MATHEMATICS EDUCATION FOR" INFERIOR STUDENTS WITH NO BRAINS:" A CASE STUDY OF A STUDENT WITH AUTISM AND HIS PEER. Journal of Ethnographic & Qualitative Research, 11(3).

Tan, P., & Alant, E. (2018). Using peer-mediated instruction to support communication involving a student with autism during mathematics activities: A case study. Assistive Technology, 30(1), 9-15.

Tan, P., & Kastberg, S. (2017). Calling for Research Collaborations and the Use of Dis/ability Studies in Mathematics Education. Journal of Urban Mathematics Education, 10(2), 25-38.

Truman, J. V. (2017, August 8). Mathematical reasoning among adults on the autism spectrum: Case studies with mathematically experienced participants (Thesis). Education: Faculty of Education. Retrieved from http://summit.sfu.ca/item/17501

Woodward, J., & Montague, M. (2002). Meeting the challenge of mathematics reform for students with LD. Journal of Special Education, 36(2), 89-101.

One of the most important agents of change in special education is paraprofessionals. These dedicated professionals are often the mediators between classroom teachers and our students with disabilities. They help create access for the child to the curriculum. Unfortunately, paraprofessionals are almost never given planning time with teachers, and are not usually allowed access to professional development. In mathematics, this can mean that the paraprofessional and the mathematics teacher have different ideas about what and how the student should be engaged in mathematics.

Judy Storeygard (author of several excellent texts on mathematics teaching for students with learning differences and/or special education services ( Count Me In and My Kids Can) has been working with colleagues on addressing the issue of access for paraprofessionals. Funded by the National Science Foundation, they have provided a pilot program for paraprofessionals in the Boston Public Schools, designed to increase access for paraprofessionals to high-quality professional development in mathematics. I would love to see more projects like this!

Check out this video: http://stemforall2018.videohall.com/presentations/1095

One of the presenters, Karen Mutch-Jones, wrote the following in a comment on the video linked above. She was describing preliminary findings about what was important in designing this kind of professional development for paraprofessionals.

1) Paras need opportunities, over time, to immerse themselves in mathematics activities that help them to develop their mathematical thinking. Often, they have not had positive experiences learning math themselves, and so as part of this process, they are developing their math confidence. Many have become quite excited about doing math!

2) Our paras (and other paras we have spoken with) can identify the ways in which math instruction is quite different than what they experienced as students-but since many haven't been involved in a teacher education program, they aren't always sure about what it means to instruct with an inquiry-oriented curricula or resources. Understanding the goals of such curricula and experiencing inquiry approaches within their PD have been important to them. Also, they have been eager to learn and try out instructional strategies in their classrooms (e.g., how to listen for student thinking, asking questions that provide students with new challenges within an activity, asking students to re-tell the story problem), and then return to PD to debrief with each other and us.

3) Follow-up activities have also been helpful. Through our project, the paras have had opportunities to plan with their teachers and reflect on their students' math learning and struggles.

4) And last, but not least, the paraeducators have created a math learning community where they provide each other with support, encouragement, and new ideas. They are incredible resources for each other!

Here are more details about their grant:

Over one million para educators currently assist in classrooms, and another 100,000 are likely to be added in the next ten years. Para educators are often required to teach content, such as mathematics, but there are few efforts to provide them with the knowledge or supervision they need to be effective when working with a range of students, including those with disabilities and for whom English is a second language. While professional development will enable paras to make a greater difference in the classroom it may also increase their access to continuing education and workplace opportunities. Our project is designed to develop, pilot, study, and refine PD, that focuses on developing the confidence, mathematics knowledge, and teaching strategies of para educators, grades K-3 in the Boston Public Schools, as well as providing support for their collaborating teachers.

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On Saturday, 11/5/16 I did a presentation at PME-NA in Tucson about a research review I recently did on increasing the participation of students with LD in mathematical problem solving and discussion. The basic idea is this: why is intervention in mathematics always focused on content. Could we also design intervention in participation?

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SageMathCell project is an easy-to-use web interface to a free open-source mathematics software system SageMath.