mgonzalezAnonymous202020-02-09T09:53:00Z2020-02-09T09:53:00Z2020-02-09T09:53:00Z15485426697222623148916

Enseñanza de la Matemática mediada por la tecnología

Mathematics Teaching mediated by technology

Luis Alberto García- González

Armando Solano- Suarez

School Technological Central Technical Institute, Bogotá, Colombia

ORCID:

https://orcid.org/0000-0003-0420-8493

https://orcid.org/0000-0002-4740-2977

Correo electrónico(s):

lagaciag@itc.edu.co

armando@lasalle.org.co

Received:

February 22 2018

Accepted:

September 9 2019

Resumen

El uso de las Tecnologías de la Información y las Comunicaciones en la educación, específicamente los Ambientes Virtuales de Aprendizaje, le han dado un nuevo matiz al proceso de apropiación del conocimiento por los estudiantes y el modo de enseñar por los docentes. Se realiza una reflexión sobre diferentes estudios basados en el uso de las Tecnologías de la Información y las Comunicaciones y con ello los Ambientes Virtuales de Aprendizaje, en el proceso de enseñanza-aprendizaje de la Matemática, dando importancia a la metodología b-learning dadas las bondades demostradas en los últimos años.

Palabras clave:

Ambientes Virtuales de Aprendizaje, Enseñanza de la Matemática, Tecnologías de la Información y las Comunicaciones, Aprendizaje

EduSol

Vol. 20.

Núm.70

ISSN: 1729-8091

Published online: January of 2020 (http://edusol.cug.co.cu)iVBORw0KGgoAAAANSUhEUgAAAboAAACOCAYAAABHa82KAAAAAXNSR0IArs4c6QAAAARnQU1BAACx jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAAlwSFlz AAAh1QAAIdUBBJy0nQAAQr9JREFUeF7tfQmYXEXVdieZnpksoIBASHqSsGg0CuqHy4eKfKgooiDw IyibIPALIhi2DwRlEdmVRWRHUDYBk8lkAREEBGRHCWHf9zUQErbsk+99q6t7qm/Xvbfq9r29zZnn 6ad7uuvW8tby1jl1zqnc9Hz+6OtyuVVz8heKwFW53PBp+fwxN+dyowQmQUAQEAQEgRZDoC+ffwKL +Mt9nZ3brMjlhrRY9TOv7syOjo2Bz8PAZ/G1udzKmRcoBQgCgoAgIAikiwCJDov4Crz6saBPndLd PT7dElozN5Da6sDkQryWaXyE6FqzK6XWgoAgMNgRMIiOZLdiWmfnO72dnb+gum4wYnNfLpfv7ej4 GXCYqwlO4SIS3WAcDdJmQUAQaAsEgkRXWtwh3T2N1w6DRZ3JdqLtW2k1ZYnczHeR6NpixEsjBAFB YNAhEEZ0hjRzz/Surs3blfDYrmldXV9He28PSHBBshOiG3SzQxosCAgCbYGAA9GVFnwSwXeuzuWG tUPD2Q6oJ7fA67YYghPVZTt0uLRBEBAEBi8CHkRXOsN7AM/sPiOXG9GKqP09lxsJ9eSeILgHHAlO iK4VO1rqLAgIAoJACQFfojPO8N7As6fAcOUTrYAmyG393nz+NLwHjUxs53FyRtcKnSp1FAQEAUHA BYGkRGdIQ8vx+U6cc+3XN3z4GJcy65WGrhKQ3A5C/e7De7+nBCdndPXqKClHEBAEBIEsEQABHErT +RpJoKTWJOndTvcEEOhnEUmkI8u6B/PGuVtnX0fHF1GHo9Cue1MgtxLZLUde59e7PfXETsoSBAQB QaCtESApUepJg+wCebyOvKfhu0NmDhv2PzNGjfpIWtabyGforBEjRkOS/BaI9Zco5xqQ0bzU25DP PwWr083aegBI4wQBQUAQGAwI0FEaRHEwiGJB6mRRdLimM/pSENILeP2DEhK++yVibe4BovrejI6O TSCNfY5nafjuk3htgO8+39fVtSl+33ZaR8dP8NvReO4ivG5BHq/gnRKk6xmbb7qFKO94Gq8Mhv6X NgoCgoAgMGgQmNbd3QPyuDJFtZ8vwTQ+PaTDVjGyGTQDUxoqCAgCgkDaCECC2hiEd3eGElPjCa1a GpxNVSiwlODWaQ8oyU8QEAQEgWZE4Cicg8Ekf/uIsFjNSFb+dcrnH4cqdKd2cYZvxrEkdRIEBAFB oKkRoLUhiQDqzAfbScJDex5Cu3bl+WRTd4BUThAQBAQBQaA+CCjCQ+BjkMPNeM/SEMRfKnM3SlkO CfUmtgMSa13dH+rTS1KKICAICAKCQBoIDJmZz38aEtE5IIy3W0TKewsEdyatOuUMLo0hIHkIAoKA IDBIENCxI3fUfmypOJ6nSJwf0I9vemfn9wfr/XqDZBhKMwUBQUAQCEeAztBpOXGDTFaF/9vOIKqr aogpWYvakrekv4ryL6ERDW4JXzmtvsdlrJtAddudVn6SjyAgCAgCgkCdEAAxPIlX39ThwwtpFkkD j6l0+O7sPBBS1RSU8Rw+L0tRWqMD+hLG6sT7FSDsn9HJPG3LyWm53IdR53NRxsJLUyTONLGWvAQB QUAQEAQiECDR6agl8xCZZO+0iaJUNKXGqSNHroEyvgpy2gukdALKvRwEcpOy5mTElM7ON/SZ33y8 M5wXQ4g9h99no543wIn7Ejx3LD7vBglrI0qQWXUu64uytkf5L2pyXixElxXakq8gIAgIAhkiUCK6 kqQFUrmLobcyLDIs6yEkWUqCDM6s3xtyyStDkAGX6wPS5+K+XG6lBuAiRQoCgoAgIAjUggAW9Kcs 6kSqGC9OW51ZSz3r8aySOPP5s5RKtNpdQYiuHp0gZQgCgoAgkDYCWNhtRFcyCHmPgY17c7nV0i63 mfLjOZwOGB0V0FqIrpk6TeoiCAgCgoArAjFEV7p1YB6JYEYu9xHXfFshHQkcktuReL3pYCQjRNcK nSp1FAQEAUEgiIAL0RkkMB+EdyosHNduZSRndXWtg3O436FdNHpxdWcQomvlTpe6CwKCwOBFAMT1 tMdiX5LwluC5Xu2DN7QV0KOhC6w2vw1i70N7bWdwcYQnRNcKHS11FAQEAUHAItF5E51JjCC8Z/A6 Bt9NTMvxPK1eYn0QquxTPGcEwT3vS+hBq0s4jI9Kq26SjyAgCAgCgkCdEAAB1ER0hltCv/Z3OxrE siEDQNepCRXF0DUBd+l9Ce06LuXrhRYjbyG6RnSqlCkIeCDQ09Nz9Pienj+MKxROGz9mzEYej7ZE 0vFjx/4P2nY624jXL1Dppr0/E3X99vhC4Qxd18kNA5gSWY2Sjl3ll8+/AuL7y/SOjn1QxmeyCp91 SS43kn5/KGsy1al4n5tJezo7G0J0HCjjenqm4XUNBsxV66yzzofSGCyYKMchv5l4zcAgPDyNPLPI A/X8Gdrey/bjcx/qe1AW5Uie6SGA8XREacyq90Jhj/Ryj81pCMp8B3VYoV+NW1xjq5osAfA80mjf S81MdKjrqeW6FgoPJ2txCk9lRnTVRh403b8bRHQRXofi83aIkvLFGd3d4yApfSgsIst5cCC/PJdb hQYwWlL7AZ49Aq9L8bofeb2fEbFVEDjKWdQIiQ4D5WBjUPePGzdurRS6PQfC+LeR741p5JlFHli0 /mbUcwX+/2cW5Uie6SGAMfsfs8+4QUsv99ichOhiIapfgsFIdFbJDwTSD6JaTMLC6y2oHF8B+b6k 3othwD7QxiNMF2cwktnvQnT1mxxmSVgkbwwQ3R2NqYmU6ooA+uyhQJ/BVbVuf0J0dYM6viAhugaS VhLCFKKLH9RZpMCi+feAdHBbFuVInukhAKl7dqDP/ppe7rE5CdHFQlS/BE1DdJCcnk2y8A+2Z0h0 vHuvfkOkWNJgV12C6K7EorlML5zLeaZY7z6Q8vwQANHdjP5aXu6znp4L/HKoKbUQXU3wpfuwEF0L SnRCdOlOApfcCoXCcBjgrAFLujFrr732mmuttdYIl+ckTeMQYB+V+ozv48ePr+c9jkJ0jev6qpKF 6ITonIbjYJfonECSRILAAAJCdE00GoToWpDo6MpQ7zEkRFdvxKW8FkdAiK6JOlCITojOaTgK0TnB JIkEgRICQnRNNBaahuhgyv/cYDMsSdJeGqOIRNdEM0iqIgjYERCia6KR0TREB6tLIToH6ZJEB3O/ uhtCiETXRLNWqtIKCAjRNVEvCdE5kEsSySurZ4TocjlYPn4OkVm+gdeXJ02a1BmcT+uNHr06TMr3 hnn5X/C6C6/78boFrz/CLWDHNddc0/mMk5Z7KGeS7TVmzBjrRcCo37oImbZpqY4+5dnWhk022aQD FoMbMb8JhcImYeVanh2CZzbEJP8l8JiC9t9J3zK+A4er8f0hE8aMmZhkPVpvvfVWhiXqV3UbJ9ny oJXj2mPGfGztQuELiPX42bhyVl999VHAbVu1KBUKs1Dnu5UvXKFwL76jH+N5KhQb2rRJRAxb1i2s z2oNXYc2j2UoMdTlArxuZPQVHYGF4+tyYo0++paqQ7IQYENQxnpo8w+Q12+QxxUsB//fp/0C79Fh +E7HONu+1vYE+4TzCdh9TZWNUHd6/nDM3K375Ay8785+xe9HNTIEGDDuItaoxwk6hKAaL6wz/+c4 Qlt2wWudtIiO6wHHKONmopzrVL8UClxf6MpyHtcX9n3oWIfqstao/plFI8mKtJLkK0SnfPoGYgiO H19eQEkoGGgnYsC9V+EoPBBvUMUdxPOvcpGIW3j5O9JtFZpXSLxLpJ8ceOZAl7LC0mCiftcMvzZh 7NhPx+WHem+sJnxPT38UFso3sFCYPnbs2I/G5Wn+jvy3LOULPB8J/PYVLpL4/V0jzaLVVlttpZAy OrB4HIa0b8XUtRQ3cgXq/AoI4fO2/MaNHbtXWD6o104+7SylXXvs2A2A51Q8v8Sxju8bPnys92SX cpH/dIc+K+OA9Auw2B9fq7sLNyVaa/OiY/s4rsx5VrdYl9wQoa6/wus1x7rSl5L9UcQtQazLDTfc ME98MAbeiC2zUJjH+pGIq/pciM4trJgQXYDoIDlxMIEM1sYAfDB2EA6QHifqPnGLD/L9vi/R0c8O A31ReZHHbjiunKjf9a6+NEnvQ9qoKPFDUe6vA4vsAEEESN9o23to63au9TSJjqSjnxuKdh8XUnY/ Je0q6RuLAdp3rUe/ldrST8nHSnSQ+tIiOkqOxBPtWpqgjibubkSHwOGJykHMWBu+Lv2ppP6enscS lTswnupCdBh33EQ9W1NdPYmOvrNKCxI+d+zzC9IeNpCFij4QonMjOkiBCwf7GZ0p0WGSfoeDCQPx +cBAnIvvuGicgtdJ+DwtsAOlZLcoTjpC/l/nQl5+mRJSxA0GWqIpTYDlYYty3EI0EVIQ6l2WYCGt 7B/xzBCUe1rVhCwUnsF3vEplH0o0+v1stOllMy0wWorvtomrk5Z0TYluAb4jyVWXrRcHSkI2NZuu lymhLKFKSO/Y92B98dpT/38lfnsOz3CTwoV1mK2uE3p6dij1F6V3nb4kzTtLdNyR49kplgXufV3H 49kfKOunSHMYyjpHqfoKhYWWZ5yIDs8dwWcpOegyGHX/AKoLFRZFafUkvOZY+vkG9oNL/5XSIN/N g/OCeCniKxSoKv5ftg+Y/hyfT1DjmvOhWlOQOdFxI2ZuIHX7ORYexPdna4l0H/xPjcpJqOdMtON1 C07OtxesvcYaa1o2Acvw3T/VNUzsF6pHgRNeVJcuDsypxyBtf6TcJylcSDooVJckOkQTHu4zmNNI qwdReTfdyNsLTKLjWQZet5cGl1rYCoUfM5JJsN3cmfUUCjdUDETPUF7If0H5+QiiI2EEJhjv6/L+ Qz4/NNq2OGrXzgkXWNTnEwsUmrcVrM4bitJfWVpB++ZPGD16fFxFA6rLRZpAB9SkJNdx407Ewvz/ lBoV56lBSRTqsk+YZaOuT+M8b/2YsoeOX2utj/PaqLg68nd1VmYsPqyny3NMg8Xsj4GxwnYeHyc5 oa2rKFLq6TEXPSei47wCLlTHx92jOZSEXjEeuakYP35b1/bxrBvtK6uXNcHezXvmYghzmD77NeO/ Zkp0+u67spZE1/WfPLsOjqtA+6kW/2+MrduMeetKdEPx3PUB4roranPMs0s8c2vgmd5yHUF0LyQ5 sxqEzyzEXSNCdCVJoafnDmMA30cyi5ro+hzvYWMgLoNxR4/r4uBMdMUzj/JukofkMRPSWgUeqpeJ DhJqWD1poIJ0cw1SnM+FzKVdWDB/hOdKMSEpTVwR91wF0eGcD21V5yUkFW6KbEZCwTw1yZY2T8u4 eMaV6/t7UqKjUUFgsXod9fuSR/l1sbpUF4pW9t11LnXkPEA/Px7YjP2BZ1Euz6uNQJ3uo+PGAfU0 zw77ueFAFawSva3+SO99Hx3GOOeFeS58vctZqDrv5L2dxrM0mlH1EqJzV10K0RnGKAMHzE/H7bRL EyB47oaF/icek9tJomN+GOi80diUgq3WiWFlfwwqD1MNhnp+Lywtyjk2IH04Sy66rrQiLNV1KS3V ojCpOKMznsP3oXUM5meezeFzTeeYYXVNQnTK+rNSrftBmOFLBEZ1ITpFOJVnnO/btBlV2MNYIjBe /oQ0XjeE143oCoXfBQj5DNf5Wp7znkSHHVeeGgZjE/1KhQoypgLog1VLmz+dR/GuTSE6IToMCKeL VytUl8VFtp/m/K6DnwuBmQc+X+z6rKtEpxagceP+KzBBj3EtRz9fth6kStZqxYWE/N6cVPh8p085 TKsO3CvPFyJve7cRHb47yadckpshgV7p86xr2iREx/OoAAn8r2t5Rrq6ER3quptZX4zvSPWvInLD whX9/uwkfOfbxnoQ3eiiq5BpMflQ2DyIqr+vRAeS2zowd/f2xQd5HGRuHkGU44ToHP35YHUpqkvT vaCoLsOFDn5/eGZAj44zPtenfYhOkVVPzwOG6vFRfOVsLIBnbzKI4LSwOmJh+1ZAxbKja3vMdMiD vmtFo42YG9QtRPceJVCfclHGLa7l+eRrpk1AdEOwQJkXtr6U8NaDuhEdXR8C/b95FF5BYsSY3iMJ vvUgOtS10lUHPmwJ6+qlusTY/Isx9952UVkG66XOW3t6BtxRYLiSg9Xli4PwvM3bgEaILuBeUPSL 2dp38GMAXmioJZ52fd6X6FDGgcYi1K8NDWKLo2Mynivdf7cCDtefCXsIdSqrdpSqc/z4D8cWYElg 7kDZzqjzmiDR0arVt0y073wDmyVRbfTNu5Tel+joaK40BAPWor9JWHbdiE5dQWTWGQZAkUQHa0Sj ffNdVJ22/OpCdJVGJHRjiTPSsTbdU6IbZlpr4tnE2gbgXHZ5Qj5nU6ITonOQ6kh0N+dy9bxXSw0c GhiYC3azWF1iQL6bJPII2kN/r5LJ+WtootP5hC/REacKlSAsEV0WTtTtAKN+90fVDwT1L4O073XJ 35aGB+ZmH68bYaRjkegm+5YbKI9S5PNYdL/gm09Uem+iKxT2NaWjBGdzperUjei4sakgOvh+hmFC IyGMl3nGeLk6Kd5ZEx1da8wzatT7/Brq6izRMXhCYLOzb+JyDckQ9b9BiM6B5CjxCtEFJDqoIJMM Qgzkww212RvIw0ml6Et0rBv9eYyF5RkHUh2C9PeUngGpRJEIVW3lhcvnvDGIW1AFxjPGMGyDRIf/ N0vQD0NBbn+rULvB1QHfXW5zR0iQv7d7gelSgM8LkpwH6XqmRnRKBYYzaO1Kszuw3pUGVcrHEy4a 3JC4Ep1yzTCtAXEemQRXvfk90sgrdfcC5RZQWdcf1VBXZ6Kj0VdFuQi7l0a5GE9zhOiE6Chd+Ruj FArnJhmEGMyH1ovo6EtWsZhjAkfVmfEnkV6Z+4O4FjHSSlh6OmGbeWtH379iUfR+0UHZzItRKFyJ jiq/JP2g3CIQQSJAdqVzQjqHnwyp6lMOmwNr8b4SXYUPFKKNJGlTGkSnIv1A+kf7n7RhE/UdSTCs 3vjNDCe3Av9/I2kbs5botF9o2bzf1V3G1h4f1eWEceP2r5hTjLOaYD7xGZT7qJHXkzyje0nO6OIt LynRwUSw4arLOH8118mDgfAfYyB4Ex2eP8q1LDNdPYlO+9WYPm6hhiXBnTLa1xfVProB+C6Erumj /MaCEl1VqCOPTlE+XQzAa48oUrSqhcGQXsCdfadYBW+i6+l5orwBQtxJj2YEkyaS6HguivIZcswW XcUllBvJK5zoAnFAkwb1rodEBwwOMcZqfy3HJT5ER/xd54hPOmwknxCi85DoGkF06NDymRE7dx2a yqbwV2HhhigELlli0A4EdY6IThIpNdVRomM9gNmZxqR4gTcShNSPYbweKaeNCclFacdnsnmlNQJm B+saJLooqdOlT5lGq+B+jQUhKpYho2FMcM3Tk+gYCYPhrUpxRXH1Y+I/b6LjhsgMEBCQKhbzDBOv +5HmXjVvUFcbIUYRHfI0jaNIimslbWHWEh3qWvYN5Tl35K0AMY3wJDqGDXTaVPikowU2VZci0TmQ XaMkOjpVV0y8hKqq4HjEAKR6qrSwOO2gK4gOBJxkotZTomP9aNSgJBPdVl63Y6u39r1T6dDO1+NM 20E4n6zol56ei/Dd9mm8aAwQhm0WRGeUxbBNm2JhuAgYzK9aTLDAu0oivkQXsLZz9q+04ORNdCj7 rEBbGZrtMhrt6DihQYOpoTR7p9+cObYiJTrGrjQW8XXWXHONJPOnThLd8YZ0vYj+fzXU1fmMDmWa RLccGwqei9Y8p3im2gpE9wFUq7OhYu3F60x8PgqvA/u6uvad3tGxz7Surv1AQof25vMn4ftL8Plf eL2TgTr2g2tzuerrH5KOAMfnVKBcY4JgciU+oDWKpBnvQMDiQuFPLtVpRaJDu2hgUmlqbGks0pxs 4BwbAUKd5VSGKTrIBcNa02RMdOXqcXFTDtympWDRz+8BF0MRT6KjYU850DV9qWrAyYvo9EbIDMP2 Iu/xcynfx+oyqJnxCX9n2aRma4zS03OMQXSM1rOKCx7WDaRHZBSUebQxp/p9IqLE1g/k8XIGpODt p1aqA6/DgZR5Hf7fH++fxd0ozjHgSo2F3W7n9K6uzZDHxchvQUrtawzR4ZJNc0Gl5Vdsp8Yk0FEP zMj1J7jk2aJEV+GiQWnN4qdG4i9LuFFWjyWcdJQLE0PGAMz8r15EV2oI1ZUYfxWGGS6h2zyJjn1k qo15G0DSPy+io6WpMb8YcowGOE5/XkQH6aRiYxShno4rvA6qy4rjEm7q4uoU9ruP6hJpK1xMGKg5 ablVzzUL0aEez03v7Dxo6siRiUV6GyggvQ8h7z1Bdnfj1V8D6TWE6GhsYKpH8Nkr3JMNE0Ykr1C7 4aDcZUC1KtHp26nLEe3LgV51oxnlv7yDpT7f7Y8Lqhk8uhYpxK1EpKo30bFivKUc+AzctBATvYXP +BIdfZ0MVfpTyMLJv9ICnDPRaQOUNw3p5WznjiAuHn506LdvBuZcpHN5VD2yJjqqCyvqStVfwj8v osPVX2a5wXmasArFx5qA6N6G1DU5a2fsFZg4aOsuILq3E5JdQ4gOXdShzowGztNuq6nDOUF7en5R MaDGjv2iS56tSnRsG+pejmrOMyizvfjtbAMP51vJsTj/wyDIx2pYnF3gV2kaQXSK7My2Fgpvx1XY m+gqjYaWMupIXBkhvzsT3YQJE8YHtCVb+pTpQ3S6LDPyi5MWxVafrIku6NfZM3bsoT64BOaW8xmd xqisRuY6lbTcquew+L+ScOFPrJ4sqynz+eundXc7X9WCWEcfRn0/A2LcAmdyOyOfbfCaBDt3J6dj Nr63q2tdPHNfXJtRzmso53yoT3eans9vAGsN+lQl3WXW1F+m4zMG+ZJaLe1oMm5M8Pddzlw0WQxY XbaIMUoJeBoKGG1+q2RsogIz9/SUr7rxcd9AfuWzDHxejmfXramjHR5uFNFh3JmXuy6Lu1bGl+iQ Py+mNVXBXrdAGNA5E502QBooM8JR39Y1PkSH53kD/QvGxmi2Q3dbk2RNdOriWzMYgoMEH9YWH4mO 66tpJBcX99ULPyzkjSC6fhiTnAKCcoqfhvO2tVHPKSCeJRaC6sdvT/XCMAVqSidfH94UjnyuNPNC 3svx/xzk9VvUbdPzEpwNegHvkRiDjjcpm2a3kRHuo7Lm5YVclI38ZrpWpZUlOmVCbkSOB2FspSSV 4r1iJetTZyz4bNCiE/gkjc/o2gUNk+jMBYsm51y4oyrtS3RIvzryLV/wycDTzqBUJnQmOj0XTKLz uffOS3WpxhpuDq+YxzEBDCLII1NjFF3Xq4y6Lh8/evQnkvSHJ9FR2/QHo1zeWZnOOV29iQ6EwnOy w1xBm9bR8SU881acBKZ+pxFLLhdqmm2WSSkQzxyJZ05C/lvDonJ11zrVOx0ce9cwFwEu2An9cBj6 qSIKBybfD13b08pExzaaZuT4rC45RfsvKe+yY4LyWnAaCkwGbklAQOZaHLhd+qFREh1wKt8UDewe j6urL9Gpvhg37mpjkaOz+jZx5Vh+dyY6bH5GB86inM6qS2V6SnQ5WnOiPPM2eIbRc9rsm+3MWqJj WQwtV0HKhcKsuM2Nra98iW6d4u3rJkZTkG/tmrR6Ex3Kc7ZOm9LZ+VGQ0ZtOJFfyhcvnr/FRZSaY SA15hOdKFZOyp+dmzyssqBYoB1RmXrQ0dFVbKqKovKanJfzozM7CDv6LpUmEtiygL5PhZjE3znfO 1vEqDmKlm8FtCOCb2O8obnA1gugYrsrUAgC7c+LqmYTotCpx4OYIbOgodcWVFfjdmejw3LAKt4ZC 4Q5+51qeL9FxwQ5uNGFwwWg9zkcveh5mLtGxTqjrnQEJ9Ghf0vElOo1RRRxWurm49kloOpxFvepF JA7O1WH54VxtBoxCnDoVxikdkLTuTFS3fH73moFpsgxo5m36vmmiuttlIaCUQd+kgPqT0Rl29mlm qxMdJ29FRJienr8amJzpg4WRlnkOWAwWNxB34WB9ok9+mmRjd65pEB0cMZ2lCIYjA0blMGr4vMzF /SIJ0alFPOi8zbMibCY8FlgfoqOqrEKdyM2gK/EkIDqqOz+BMgcuNC0GKLhyPVx06jpe6iHRsS6Q QD9PNXWFlI1rtnz86hIQnQ2j5SjzRN9rjSrS14voaN15lYd6EKS4VyKSKxLxQ+0o1WHC/7hCrC9K Ekvx/Y0gvEPVIjh+/EaUXLAL+iYG2X5YOKbivTp+X6GA7nDbdJQmYBsQHVUy5aDS5gTmpHZdaILp 9B12z1dI3MAceF1sRNcIPjYMz62HwNM7a/Xpmy535qVBdCp+Je6x49kvA/YGI7GoGKHjxn0Z7bmA xk+BDdIFLjglJTp1C71xA3pZrQzpAnXZk5Z5NtLjNTjrAk+0Z4eAmn9yVH0Z6SWQnvcs3oDX5hEL 61A6fAOnbc35GBUZxawD5uaPTAlZtRGETlIg7mHl0oGarjBIN8Pok9RvLzDrivow0PKAKrG4kXsD 9T2RqtgQjdAQakuUGxPWpnJdC4WHXcYO0wCjXYMYaV/Xw2kVatusMXYr1z7gcwgNWfD8PeWxUi+i g49caMDTYONJUqjXkzUQ3QpaZ7qC2krp0HlHWMjOLz4cooJ7qj0VRO1AdNqnruwTpifhgx4Sg3W4 rIO7tDC5yoGJA+SwDNi9ikn/ML5/EJ8ZU/IDSz/uEzcWayU6fUNDxcJFKQ2vt1D/53UcR3MXP2Cs gcXDddwkJTq2H320ql6obOO6H/jN5zkh6jwHnx816hxsF5+PJDqWhzR7VxFPUdJajLyfUsTLuwcZ 67LoPE+JrKosV6LTc2mPgLRkWpwyviYtNB9UGohC4RmtzTGNyErpMyU6jQ9vGzdVymZdF6EdDLag 6sqxjbq+a8OT4z9ufAdIdi/LRqtU9gfERc+nRzi/UG7FvMZ3SydOnFi02cCZWeaqS5DOP+nH5tpI hPb6ci0kx2eh9qxLSCbXNqWZDjsl7iRfCiymsWSnJbtj40zDw+raDkSnFpnAXWxo18Fp9I9WZV0Y nHAe/XRyXD1qJTqLBW/suOEiB4zO9lEd1UJ0xEA7cx+Ochd44GdrSyzRsTxIENsrSaWGoMI+RMcy KU1TzV1LmVwHat2kxY05XdeNUdf7a6qrJ9EpkoVlag3l9jMmrWof/cVqJRWH572sp+C3dqxDnpF+ fL1wH3DpwFIauhzQX64R8Sx96llKOwmxCLEI7IvXHVWql8rJulxJGrxjyyP6vK1OKOdWtZOmZFI8 N/H+w51Tu/B5vSP/BzJwOrNF+luMsnf0Lth4AAsS7wZ7UklZ2In6+M65lMvJhXzPVBKSZedvLBaU CuYCj+l4380leC7y/oraxaJPuQD4nJew7jiv3QDlnUdJBfkEJdsgUcyl+tVFpRrEZYMNNhhJSUiN Pez0k0a54NkV6nkA8rgV7+/FLbTczFHKw+vPeGZ33rvn0mdMQyyV2gtXWEVIEiWMKF29qYnqQqTf L7ElNIx98PyfkB+lOJvUZvYL5/PrVK9iLBztGpfTFYOYdMPQxu+g/MtRPmOT2iToyroWJa2/oX2/ ZISdhPXo4N2SyOcaLdlGbc54gfDjeJ1FNW95E1AHonv/77ncSJ8GQsq8vlaig0TnGspJVY2RWVDm PLzewrN/ge/e5q5+eT5tyyKtkiS48+HtxzjHwPv/x/tOGBxfo6qu3NlZFC55RiEwjJsLhn9Cn+yi +2VPbhLYN/wtqXSdAuxDGPNUWaIWCluTaFHPn3D8UGPAyPw+Frkp1Cc2C57B8HyGPpAV9QWeyhwe hh5RNz/EFmAkIDZqU8G+GjduL/Yd/t+VZQObL9A1AcmdjXocyx6mQv4VbzX/Yalcnlfx9m11/lS8 3sfZMtSx3CTJhk0YPRr7Z9y2XijsqMZ2JUaf14EtUq0rVefK/5FjFjYLHLPc0OC1DUlfB4Ku1h5m TXQgDa8ArVRxguheSIHo5vuoS9nTKHdGRbn5/KOMk8kg0UlGgjwjCAgCgoAg0AQIZE50+fwxPs2E KeBwkA2v5qkpxBgIdikDOvuUzet+bOUCoxfx2zlZx+P0qaukFQQEAUFAEHBEAAv767WSStTzsLbc 1rEqKhnI5MMp1affJ44my57R1fXNiLIX4/xuZZ+2SFpBQBAQBASBJkAga6Kbms97RTaYPnLkmikR HSXCST4Qq5iaIZIk42z6Sog+ZUtaQUAQEAQEgYwQyJrorh4xgoe2zn+wfvxIakSHi1udCy5KkzRI sd5ZJ0Tng6SkFQQEAUGgiRDImOiW8Wodn+ZCahqFOi1Lg+xmdHR4RbtgeDIQ2kLrOZ1IdD7dKGkF AUFAEGgeBLCwv5EGqYSQQ79P2C+i8hAsHFGnd1KpU0fH53yQJtFFGMIsgfmol3GLT9mSVhAQBAQB QSAjBLIkOhWhJJ9f36fq2r0glTvyZubzn/IpG6HLh+trhGwWn0t8pVOfsiWtICAICAKCQEYIgIwy k+iUVIYbun2rDnJ8OAWJztvqksYrEeUK0fl2pKQXBAQBQaAZEIAEMzcFUgn1eUP+f/RtJ+pza611 QrmL6JPnUzYsRHcVovNBTNIKAoKAINACCNSB6Ob6xo8E2VxZK9FBknzKF35gcZkQnS9qkl4QEAQE gSZHIGuiI3EgWLLXBZ945ohaiQ6O6jDgdP+jMzjKnB/hR7cUd8mv4p6jpBQEBAFBQBBoCgTqQXQo 46Hzcrm8a4Onwi2gVqLr7eiIvdvLrA+cxX8WVSZDignRufagpBMEBAFBoIkQwOL+Zq2k4vJ8b1eX D/EMQZ6zXfINSbP4quHDGbXf6Y+3K0DV+aIQnRNckkgQEAQEgdZCoF5Eh3LmTenqWscVHVhe7piU 6HjNjms5TIeyTogrixIdjFtW9clX0goCgoAgIAg0AQJ1JLoVuAz1ftfAyEfhrifU7c44Agr+DkJ6 H2rI9VyhhYrzK8hjSVw5QnSuiEo6QUAQEASaDIF6Ep0mk9tcHa9BjB+DtPVWHAkZvy/vzed/5Arx tK6uCSAwJ+d0Et11ItG5QivpBAFBQBBoHgSwgPsQSU13xJUICWXOntLdPd4FBfi2/RfI7uk4smPQ 5ekeBiizUD7yfTIuX6POQnQuHSZpBAFBQBBoNgQaQXQkD174CgOVb7rgcWnR9P9IPPOSRVXZD0OS 2xHAeSOXvJiGaeOMTyzlLO3N5VZzLUPSCQKCgCAgCDQJAljQ6y7RGSSyFIRzimsEk/vgosAbCfDM j0HQk/G+K9Sbn2B8TBc4eQ0P0h+F8he5SnJGumXNTnS84mhGZ+e3gc3BwOY01P1C+BP+kbejQ6V7 Ev4/EJ+3xgZjXZyBDnXBTNK0HwJU2eNseiO8fwvjYYupXV2b9SEAuuuRQvshIi1qewQaTHRFVWg+ /9ssgeaijjJ+4KOqtBBhUxKdIm8QPwjtFqpvXQicgauBxctIezGJMUvsJe/mQgDBG/ZAvy+v0ljk 80+4Hic0V4ukNoKAAwJY9Oa5LI5ZpMFi+zwkrG0dqpkoCW8En9bR8ROU80gK9W8qoiN5Y9HazabO 9WzrApHuEg2vlnsIEtzXMTYWW8bHnKm53Fot1yCpsCDgikAjiE5JHpDi+nK5lYL1hITSATXK3kjz H7wuIlFRraLTRqooqdqkawEJgCHAMKHf9Vz0o4xtllE16Iprlummjxy5JvD7WxptA8a4nUj+2h2B WVDxh5zH39Ms47rd+0Da10AE6k10KO8uWlLamozvP4XF+3bbAo7nFmFxf5bP4/0feF2D1wy+INXc gGcYSSXL88amILopnZ0fR3ufSYPkdB4Q6OSvnRHg5cchavtb5VyunXte2lZGoF5Eh3LegZry55TY gvDzZm/8diAW3g9SXMBTcYUwjVFmjBrVUIluFiLLxKoq8/kXgPX5SmULQ4O+rq5N8foGJNxtobra D+05F68H9TkNz2omyXRoLgQu5rkrtBpp1IpnuBgHt1SdyXV2Xg/V/qg0ypA8BIGmRwAT4O2syQWL 8/VQKa5tA4ORUvD79KzrkEL+y64aNWr1RnUoVbeaoMIIfA42C9+zbSQsG4sh1w4fXoAE/YNGtUfK tSNAC2IQ05+ppagVI+aFMXOJxfCkz9XSudY6yPOCQFMgkCXRYcK+C2li7zDz/96VVlqNZ3EpkFDa 0pstv8YSXWfnBSEqXfoRnsLzyaYYUFKJmhBAH6srqtIgOuTzc7xoiUvJfRk1JiRRGSs1dZE83IoI ZEh0c3ieFIUJyr64RUiOxLfs2gZJdIzHSZcAi/qpHyrJg1px3EmdqxFAX35fE1IqRKekw1zuw1NH jFiL2gioKjsFd0FgUCKQCdHl84+7RPrH4v16KxFdI1SXWv10qw0nWJeeg0Hr5Cw/KAd3CzWadzBi PrxX6uc0JLoWar5UVRDIFoEsjFFcz35QNo0i6qF2TKOMhoQA6+3utkpzUFc+w3v0sh0dkns9EJjW 3d0TDEknRFcP5KWMQYMAyGZuymSzxNVkGeVuhfKXplx+GqRmy2Nxn8XvL+uBYjMmIF6IhrJz1mU3 Y/5Qvw2b0d09DgG8v6zGTz6/A1V+MHbaDP9P5PVOWdf7PJyHgpg+i/K2gVS9PUNp8a5F11B0Zv3U pb+dnfdZDEZqNkah9SYx6Rs2bFMGZuAGlO/wS/2qvpg4c20A49TCAnhjrZbdDiH8NknLepljgZsE 5P8lcywwhi7b7WKY5TBWIjFi+cD02xyHiDK0Jd7XZ70c8s3NxOXQGLeb81kaktHtCsZ5XS7P+qRR lrf5/Gew1rJ+OzAMIOP9uq7TPmU1bVpM2BfSJBoA+arPhJ+CBQvPzDLVNmnWJ628UL/3U5o4zmMB C+oIlLugqg35/HP1Pm/BQvVd1GM2x4sKH4ZoM3g/xrkxSIjJ/Ev93Mt49kW0bTbiLG4elYeKAAMS Q/rf0YeS/RDVpwqvfH4Kyccn4gvJi2b4jNbD9uHzAyCIb5h1mwpLVeR7Bsq3+2uiX9hGjBMns321 UOfzU23twfdvoB191ldn53Y2zGjBjPQ7qbPvYjSg6E0k2op0v2e8WJ9+VPFmcbekcnUprh93BBdN tZCy/pZILDxvVn2JRdenj5QaH64yDDaB5+90WDMWoIxeEpFPOcQC9b4V5Tynxnpn5xwSUgkjfZyw Hb6/x9p3nZ2v4fujSDA2XFUbkH/Iuft7+P4y3z4JlsOxxY2YDiyxMGTOLEdZ9+K3/dve1URPiNSk IA4MgO69U6S5M3bHG3CHjB3ZPuiA/+VgQX4nQHr5Ld5Pxet0Whji/Wj8fhA+74Xffqh2i9yt4i46 DMh98NxhejJchnS34TPvnKPVWfJ2Ig+fxSCNtFysrXXO549LI3+fPDSuFfhxkfbJA31xhUVy2SMq D31zRaJ+Q/2u567ZpY7cSQcXZQYALz1LCRq/z3cZQyj3Md6lGFcux7ZLfsE0qMtZtrxJHEnywzNL MO9Odt08oR+3qKpTR8cXWCfmgfr9Hr9XxdMMGctTEJllRBxW/J3pbOTg0mZgcyOlL5dymCaoacLz v+H3l0ACx2+MuuQyJm/tM7RAemPDDVuVYZklvw9Q5i6u9TXT/RXrKDcSjnUsxRt+MctwjEnakeoz AMMaicQLpMpO/8B14KbakIjMuJubNWLEaO7KQHrHoW1UFfkS3/31qm+pHNT1eFs/wApTLSr1/GsU 0TGYACZt8lBuiKZDVWccVjai480PfA59wGAGbgu3ngtYpJ6Juu0Cv+/mm2dpLJTqFWwTznM3qWHe 0tKzz0VrYSM6lLsdMUQeM33rgPz+4qIFoloaeb/pm385PbURuLkhbixYiQ5SFt0ykNd1nuVfgfyG aP/Isz2fXULpz6W+pTQqMIRh1ORZ3nJuvlz6wqdOTZEWi+k0TzBidzJQR361KRoXXokhjInJXRra /4ZT+xFqrN5tokRiqdvbjfCDahTRaaKxWp069VvRJ+2WuHMTG9HhuWu5cCTYFKk5ggWHVrFVf0pd n+yqqGK++fwZtnxp6YzfbUGbY+esgeURcePcRnRG1B2fskppKeFsFVeuHgs3uvZ7SLrb48aCjehU 2EHcielbtlLTIpg2+mxPPOsiyVXih1slqFZ3wUb3S639z/GlpNe2+gM4vrsMl4GMc/DW+OuDagEd eyxwiBwgUO2cXs8WqXMA+/nprfWsR3mnWFQJ1111yfIZOg79w0Dg/+K9euivHWmAwHOMmZ2dH8X/ G+qzqauCKidDCvpeFG42okOejyK/CmMt1gPl3USywe+sy1R8Zz03xPcLqUkIlsuwbPjtz8brpqoF FKryQJpyerT7u2Ft4ZkMnpuP9xl4P5xGDrOAD1WpKGMifTLxvj9ed9oWbTzzTty9iyES3b+CCznS zSM++rjhVNSBG5YwyZjBxWOPPEAaP0UeS5D3Hcj7ZPZ7aSzAb1eNBRh17EQpkelCiMl6xmliWjWO eHaL/izlh8+UfmZxbPLIhOSAF8/zbOvjHUhfedZeDNV3Eep/Ip65EO9Vl0obecXXl0Y5ITfR4Pt7 ULc9sIZ98mqMR95Hibx5fjeFRGypM8/utmzEOpNZmdix8izMhbx80iwJC9ycWUNqzFgvls+GYQEr v31qLMLrcZ5ZhizaF3pllFLiRkp0xMLFL5NN1RfzVvtnxkjkVqKrnBc0oLjUduanLP9CIvwQt7gu oDRj2UQksrpkAGfns7YiaVSp8HlGHlXnEKIz1wdGYDnYFmZMSTcWAysuuGFhAs260MDjOkiucZjy d85pvF61YPu3uOfDNkwqL2xCaPUbzIO3QOD3OTHr6WLkPTmoIiZWeO5PIc/i5+g/fVtL5Ua0SGJH Uf0f9rTuy+qjARjitFWYOK2a8SExt7Sw+pqVy60S10HN9DsXsTDjnHqrYxmL0rrj9rR0TAvfRhKd bxu0KXtwnL4bdf7kQHQ0TAmVOOhegP6yBSWPXaTSJDpfrJRUUS2pQ6gL/4siOvz2Pt0Zop7HHPtx yNjezbf+celRn62r2oc6xpnxRxDde9jEfzqsXGy0KDFb10iSeZSBCTco1CJY+uOlKLKiEZ91wwJJ MQ4f/k63E2t/YCPk8nxLpKH6JwOJrnRGcVdfLjemJYDQlbwahgsYbC+amHDQ15u0qWaw9QsW8cm1 4skzCmWcgzJmYtJS5UPT9Kh8W4noSGjAzma0MDGsjVFEx7M6lwN6lHm5ZZF6NK6/Gkp0RR+0oEr6 6aREh7z2j2svF3TMKZrgB8s9Ne5Z39+1pWNVWbwSLKaNVtcM1PtXcXXA+vG4dU11OOcnfpZnl0fd GYjyaOUaJNf5lO7j6srf9TGJ7exztsu4dymj4WmUpRT08pmRXT7/GvXovn4sjQRGOyOX9ftY6B5G fWLPD9Ks8ww4j1r7BEGyay2H5zY8YzDzB+k93i5Ex3bwHK0KvwgLtjCiI07cMbtgjj7bxdJn78U9 20iio/9UUHqhVBYl/YZKdPn8U66GUsiDZ2hBw4spcVgl+R3rT5WlJH3rEhDduy4qdLTrQtvchc/o ZnH1h9P5x/Fs1blZ2BhU1pyBjTnLRvtgw+L+Z5N8WQ8a7bnn0uQp0UgeJLupJBOmU2cYEJFdzw8a DRkP0EuYoO7n17s+POO09Unc+YlLPVV0jOpF5pl2Ijq076pgG6P8hCIkuttcMGUajBlGSwmekyyP O+toJNGR0DC+55n1xv9LoiT8CNVlrMVmCUvkcbhForvRFWufdNCCXGYpawdfogOhRKp0jbYdapm7 JMnhcfXW0m455mk5n+5uqyW7NjKqIsY4Ig/Wgy5hKKuqXBja7BVX55b5XVkvJSQw7+d4OJzPnwap 6b9dfHYaBeI0RH0vLQB0Sq93PYDrpBBsD6i1Lu1AdDDrZXirSfSNRP9sjzFMZ+lt6HeEz+vb3GZ4 dheGXRjRAatfuOJNizZLny2HVcmHovLImuhYPoNGsxziRLxUmXADwvtEC9Et5fgPq3MY0SHvz7hi hf7Z3YKV86bCLEf3XehYQL3+aiG6HX2JDharP3dpHy0cLW1z9sPF888Hn58BIx5b2RQeLJur/iRH LTaBB99ZXWRccGi6NFGHy95E5keYc3h423SA6AphwJ2K9i9F+I816l1HZRhjwZKuELXWpVWJjhZ3 kHR3BQY0ofdWtychOiww33TFm2rAZiE6nsFqqek+Smg+85iqzAREt9BVbUk8bQZDXGhdsSa5qWg1 +fw1aFt1mLyYdYguKr5E5+q8rV1dguePsZaeZYkQRyVV/RWidke6at8+WIUmOVtDXtV3XsJ/0LVP mj5dX/H2apvFWBbqzGUY0DdSSmI4nWYGBzveL6KudzaijlzU0SdVCxQWiItqrU8rEh36YUssIE/7 LNjBtImILuZORbMvtIl4cM7UVaKjczHjbQKvxNFkkhAdiCNS9R0cszZrb1ei48Yc5T1Zy1hIQnSz HGOCMu+quiEwh+u8xbPVLgohREeJyyLR/du1LDMd6n2MRfJ9JEleTfsMFpFraxk4cc+iQ6j/PSsu WCmtpHhhq54IBypnU4RiwrNXoSMY5HYG1VJaHcHYiZfo38/F92cpCyQdDxO/7a/UNB0dn2OUeF/w lb68o+Mnvs+lkV4fMlepMNAmOtbW9NdqRKd3rV4huGzjMQnR8dJSV7AbTXRKoszn/x43F+N+T0J0 yNNZNacluqpzYheiQx/+AulqHgtJiM41VmY9iQ64V1n64jvsk/3/eImzhehe8s+piZ8I0SunIdEx OOnJU0eODFX/0UdEq0+vxDsjw/uHyolTVTDkEkJqcZH3sQCN87fJskuporPs1t7j+VQt5bYS0WGj QafmqHG4GDjxNoVn8U4zcjrkWsdPIqLzUFs3kug4ptH+6WFYaUzeA068seA5pOM8owm97eb6JKpL aC7d/5JIdKj3XjFrA8fCKy5jIQnR6auNYhtZT6JDv1YbXSVUNyKvyRZJ9NXYBrdSAprNoqHpqi9h 1hsX7UDFnAwJRxS380z6OwbiTa5R7RvZh5iwv7a2ESGkaqlXqxAdxw7GRlV4LXy3EH14BoNbBzci 1AhQCrNpKNqZ6IAHg0RXbwiK1yEdxHkW3OBxw6TDQVXcypBQosuU6BiYG+2rUseirovQ9jN5zGAb CzyrVFqgap897zO6ZiQ6arSCbWOotSTrA7CsjpKFjVGSvJr6GQBWdY1KUjLB4DoxLngq8p4EcKuc OROX6WEIQ8umZvcRYUxEGxa+PjLBQZeE6KjCtez2+nwGNPra65oepP+Dpf1vUhUdVy6erfLTalei 007RtjOr2+P8vvS9ZRXO9c1IdLTUtoyFeSS4uLFgI4O2kegYc7V63ZsTh4ntd2Bsuy1ldpK8mvoZ hrlKg2QwUS6Ks/rhoTnKuj+N8mrIY04jVZNxg0GbTVdF+AC+C3pXWmm1uOfDfk9CdAxcayE6L78n H6LTqjhb9Iw9Xdo9mIgOi/aGFhX34jhtCnFsFaJDG6uCHkOij40jyja2M9GhbYdY1r+34tZf2xzC nLH5G8JToc3+1OIScmuuK5nwnCTOb4iwaV+eNM4Aa8oD9U10uWG9uh64nxuikjoxaR2SEB3GxZYW oosNb2XW0YfopnR3j7ectS12vQm5DYjuJtf+DZG2nczCW4HolCq6WmpZFhe2roRfOxOddV4Cq6mI les6fgycZlepQXHptW8+LZG+1iDPIA6nu4xsh6iuZJpmurBLLJulsxiLMsTKbDHDhCWpZxKiC4n6 scQl2kOpjj5ER5WUhVifdW1vqxMd2u5sXYs5d7RFonNy9G0JorNFCYKE5zoW2pno9Cagygo1TjUb xO6qUaNWB05V7kwUSFxxbql0Wqr7d2Iycbx0FR1R7RTpccaWuH7VZVzZ7B0EkumztZe+S0mMapIQ nXaGrrrShZFJXPHzITqopTaqWrxhLehRVquf0T3m2lYsRlVGS8C6bYiOZ7KWsfCyKz7tTHTEAH39 gGVT6Oy3p/KwncGD+BoRLMO1X2tOp8IoJTTxdzkXQAUZiNTmI1aTGjIh+R1SM2AZZ8BAr7QuC1Fh Ps7ffaqQhOiYv/VM1cMR1ofoUNZES3sXw0FolEtbW0miwx1t37JIZO+4nh+jrVVm4ZhfTuenrSDR zSpegRRcG5ah7pGh1QaD6pJtxHw+wjJ+lsT5LJfwYUQbbKYfsZAl3I/b/A+7xCkJiSP0KhQTMuSd eSDpuPpjMXgj6vqLZupiLGa2QLGlyc8QSAcwMKtLnZMSnU1FhnIZ3d9JveFDdDqWZZW7CyS9n7m0 saWIDjEibWOVUq1TWy1EifwWu2yAWoHodODp6lvcOzqc4r62u0QHqYtnmNWBoOE47hKWLWRer8D4 aa9bxm2TiSoxLBYVUc3jiIO/R5lwB4juQJf8skpDE2rk/R2XhaQZ0mgT8t4YPF7FoD0dbduib/jw MabfFK1cZ8HAA/3zXRsJYEcXG8JJG4hUSZbIj07ah8YRLTZPtuC6e4ThizpVXa+CcjihY/utlYiO UiraVEXq6MsbXKS6PoTw07gE4ys+HKdhaQWiU9qEfH6mRWoh+W0VNz/bneiU6jGfPyFE4zMt7EZ2 vYH4lc0GAN/9yyewRlwfNPXvKmiqpwoTgDtdZcGQXBi8T2VFZDH5ftCKh6wkEi5+Lphp1fNipH0b nxkAmedr4RFnHIhOTyib307pot0FdNSmMzdex9DhncSL96k8T7SVj+9DiQ6S53dtbWXbqJrD++F0 lNa3F+wIFeBPUdZxKkScJdBvs/rRaVzt/YpzSbTlz2gnA4yfq9qdz1eZfOM7m8/hCjz7Pl6XUb3J +ayx2kWpO+mbls/fHFzouAlMENQ5U4dxqndtxynqO7QB2ByB991LYwG3o+xDwziuR0hT4RDPMRVn rKE3whUbh2Z0GC8RiFobOjsfClkbGAXnLGhedub1Pfi8Hdp/LPB6IiQ9HfMnNTU5pV05NPhil4XV SLMMB5tfcqkHwKb/T9Ug9CzP71wPV9XzyhKX+jVjGqr0MKAvsk36mnBzJLpLcRO5VZ+f0JAoiuh0 vM+pNbXLqFczE91USKmu7eTGJaiSogoe/fKCax5R6ZqR6DAXh6DOV6bRvnYkOq5VMzs7P4ox8Eot GKHvl+C1dTOufZnWiZIXGn6PD3hYvJ50PfviBaNI/5hP/gnTvs2o7nHqtUzBTClzTQA7YFC/mBAL W6ioWNVlqfrYXU9Iy2o2iuiUyqqolqu+LTwBsTYz0am2hvlMWtp63corrxocTsoVhXE/E2BjPtOk REfndqp4r6+1fe1KdBwPvIg16dxEv8/j0UZKy1TrZXM9znsYKNVzgN0dF36ohAQchoYj7wMSlBEv zRWtiQ5xrUsr9Q4nPlVQNW4UqNK8Hdjv6tN2OutS9YXyF3qOi5Kak2d9t7kYXPAWCaSlZdnbScrC M8uB0dPQNGwc1sawi1d9zKuTBnUu1Umflx2G+sZescPzUltbtF/V5TbVmyN27Jd7om77QN5bWPLK VHVZaislWV6Gi/Kpjouf/9U3vlPt/UzfsGGR8WJbTXVpjgX2HdSUJ6ANNgOVKsyousbrap7h+6wB bZkWg4o3EXuJxdQZc4fhCog6HMVNuuqMB88Gzw4cB/a7lADw+hWdnAfDgSpvf6CvEdrMM6vpaPfj wUFOQsJvL+H9XrxPZVw7Sjg+19DY+hGL82j64CBfngP9B6+5gX7j/YNz0XcM90bV02FTu7q+5hrV wiyT5uQ8Z0AeVKffzx0oXua54xK07TV892+0jX50R3BR5s3fceNAGft0dh6M/E/Hc+cBn98TTx+H eJTRwfbp8Xs+3/k/idp1DjAdsFmdtzag/CvwuhOvB9gm1OkfyO9CzJH94jQTlLqRltdcTeN4wOfg osdbRZ5HvrfhtwtQ3n693d1foQQdV1dllAQndX0ueB7ef8d+iXvO/J0uA3iO57i8uot4n4LXD1zz YD2RfifUn2r8/5D4zLGAz0s5FvA9fYKvpDYH79/heI8bC6wDxwKep2HX+aWx4Hp/Jtc8fT59NtuG fE5G2bFGM6W2A8sfEVOOQ43xUUkinXCThnVhf9TlGq39UX6wxEnPyVvpg+nqhuDaNy2fTpGdv//b AoC9NxcBXwC4sGHH/xUeMqPsI1H2mXqR4x1MvIfuHHx3Aha1yfi8NesXF0jatw6tmp7qTS6wnJx8 17HvhmTdHl3uMC7EJAmScJK4ey71ZL7cHLEsvHdzAcuqLJf6NHOa0nggVsZ4aOYqe9VNxkIsXFwP 1LykBbbMkxi8eF0Gd5iO0pUpJt9P/y0uTLFdklECfba1fpzJdUbFS7aCgCAgCAgCrYIA1U6Qoq5O QHY0632aKguI5xtwt591m0msSq2HMkHQd0E6/HHWZUr+goAgIAgIAm2AANVECBW2b/AsyJX8lJ64 qAa9FES0L40S0jAYuTyXWwU+NF9GvvujjKtRxqtaL/0ArdLaAHppgiAgCAgCgkA9EdAHrze6ElxU Oh4g0w8E73dQYsT7H3ioi2cOUaTKwKP5/F4888NvPJf7FYiMjrSX4/tbtbEFI56YKlMaYRxD/7N6 4iJlCQKCgCAgCLQXAnTmpLd9PfzhXE2Kl9Hyrrera932glpaIwgIAoKAINAwBNSt4TD5pUlvwOzb lZxqTodyF4LgGDJp/YYBIQULAoKAICAItDcCPL9jGDDtB/JGGmrNmDx48eD9iLZ9cK1+Ye3dM9I6 QUAQEAQEgdQRUBEnuro2haR3orJ6tERpT0SEuGIHec6gQyTPCcUvJPWukwwFAUFAEBAEkiBAh8UZ iG/JkFMqekBRzcj4dYz88CRejN7xGj358f0T+HwPPftVhAJEmcBrG567NdIfL0m75RlBQBAQBASB xiDwf9+dSnQsuKM/AAAAAElFTkSuQmCC

PAGE \* MERGEFORMAT2

Abstract

The use of Information Technology and Communications in education, specifically the Virtual Learning Environments, has given a new nuance to the process of appropriation of knowledge by students and the way of teaching by teachers. A reflection is made on different studies based on the use of Information and Communication Technologies and with it the Virtual Learning Environments, in the Mathematics teaching-learning process, giving importance to the b-learning methodology given the benefits shown in recent years

.Keywords:

Virtual Learning Environments; Mathematics Teaching; Information and Communications Technologies; Learning

Revista EduSol

Volumen 16. Número 57.

ISSN: 1729-8091

Publicada en línea:11 de enero de 2017 (http://edusol.cug.co.cu)

PAGE \* MERGEFORMAT2

Introduction

The development of Information Technology and Communications today, allows the application of mathematical concepts to the different problems that are currently present in the life of the human being. The use of Virtual Learning Environments (AVA), in educational processes, is a modality that has taken a boom due to the advantages they offer in communication among people given the need to acquire knowledge at the rate that the life of each individual allows. However, there are still limitations in theoretical support, as well

as in the most appropriate methodologies for its optimal implementation in educational practice.

Research on virtual education and the design of virtual learning environments are very diverse, so it is difficult to find meeting points that can guide their implementation in educational practice. Mathematics ‘teaching-learning process has gone through several models, such as the one raised from a theoretical perspective of mathematical knowledge, Dubinsky (1996), and Asiala et al. (1996), consider that individuals make mental constructions to obtain meanings of mathematical problems and situations; these mental constructions are developed and controlled by construction mechanisms.

In the field of Mathematics Didactics, we can mention the contribution made in Spain, Godino (2010) that tries to clarify the nature of Mathematics Didactics and its relations with other disciplines, synthesizing the main lines or perspectives of research ; reflect on the relations of Mathematics Teaching with the practice of teaching, educational technology and scientific knowledge; analyze the dependence of research problems on research paradigms and methodologies; reflect on the current state of institutional consolidation of Mathematics Teaching in the international scene.

On the dynamics of the teaching-learning process of Mathematics based on computational technologies, several authors have also researched such as Cruz and Puentes (2012), Faustino and Pérez (2013), among others, which demonstrate how important is the methodological use of the computational technologies in the mathematical formation, which contributes to reach levels of quality and effectiveness.

Another of the elements associated with the evolution in the use of ICT resources is the concept of knowledge society, which had its appearance in very early stages of technological development (Drucker, 1969), and was understood as a proposal to consider knowledge as the central axis of wealth and productivity; at present it is understood as a pluralistic concept, focused on social, economic and cultural transformations and characterized by the ease of access to information, linguistic variety and freedom of expression (Unesco, 2005).

Development

Research related to the use of virtuality in the teaching of Mathematics that has been carried out, for example, in the United States, Wellings and Levine (2009) questions the use of ICT in teaching because the studies carried out are not yet conclusive about their benefits. However, the generation of the so-called digital natives or net generation (Tapscott, 2009), have shown that the use of these technologies is undoubtedly positive today.

It is no longer important to question whether or not they should be used in the classroom, but rather how to obtain maximum benefit and study its true reach, especially when there is speculation about qualitative changes in the cognitive abilities of young people due to constant contact with the technologies (Unesco, 2013).

On the other hand, Lancheros (2014), in an investigation carried out in Colombia, suggests that there is evidence that the use of ICT encourages motivation towards education and that tools such as technological platforms (LMS-Learning Management System), such as in the case of Moodle, offer possibilities to develop new strategies for teaching and school learning, using them in a didactic way through b-learning. In this research, a b-learning model was applied through the use of the Moodle platform in students in cycle five and an increase in school performance and the acquisition of mathematical skills was demonstrated.

A documentary research carried out in Venezuela by Zambrano and Areque (2016) of a qualitative approach, resulted in the dynamics carried out by teachers through b-learning methodologies depending on the conceptual framework, the area of knowledge, the context and the socioeducational reality. They concluded that the multiple definitions of the topic usually create confusion in teachers who are interested in making use of this educational practice.

On the other hand, Balladares (2018), from the Pontifical Catholic University of Ecuador, proposes digital and informational skills to achieve a necessary educational digital inclusion inside and outside the teaching area. Believes that a digital inclusion in education offers guidance to achieve an education in diversity. A digital gap divides challenges education to

seek equal opportunities for access to information and knowledge for all. In addition, digital inclusion seeks to ensure educational quality, considering ICT as strategic allies for this purpose and promoting the development of digital and informational skills in teachers.

It is said that when an instructional model is effectively implemented, educators can facilitate a classroom that focuses efficiently and effectively on student learning and personalization of instruction to meet the unique needs of each student while preserving the pedagogical authenticity of each teacher.

In a research on academic performance carried out in Colombia, the results obtained show that, the final average grade of the students was superior in 20.33 points for the academic period where the b-learning strategy was used. It was found that student dropout between academic periods of study went from 12.33% to 2.81%; evidencing that b-learning helped improve the student retention rate. Consequently, it is concluded that the implementation of b-learning improves both the approval percentage of the course, as well as student retention, so its implementation in distance education courses is recommended. (Ángel and Castiblanco, 2019)

In the research: “Complex thinking and academic performance” by Melo and García (2018) it was obtained as a result that it is important to make a diagnosis of the advantages and disadvantages that occur in the learning of students who show the predominance of a certain style of learning, to then analyze the possible difficulties (blocks) of cognitive, affective or cultural type that may occur, bearing in mind that the first step in the treatment of these blocks is to know them and then get rid of them, which will significantly improve intellectual progress.

Principles on the School Mathematics teaching

The professional organization of the United States of America, National Council of Teachers of Mathematics (NCTM), published the text Principles and standards for school mathematics in 2000, with the intention of being a resource and a guide for general mathematical education, since the Early childhood education until middle school. Its authors propose:

The decisions taken by teachers, school administrators and other education professionals, regarding the content and nature of school mathematics, have important consequences for students and society. These decisions should be based on a solid professional guide. Principles and Standards intends to provide this guide. The Principles describe the particular characteristics of a high-quality mathematical education. The Standards describe the contents and mathematical processes that students should learn. Together, they constitute a proposal to guide educators in their efforts for the continuous improvement of the teaching of mathematics in classes, in schools and in educational systems. (NCTM, 2000, p. 11)

These principles constitute statements that reflect fundamental basic provisions to achieve a quality mathematical education. The Technological principle stands out, because when students use technological tools, they have more time to develop concepts and make modeling, they can make decisions more easily, reflect, reason and solve problems.

Although the concept of technology is much broader, since, as such, technology can also be considered a set of knowledge of a practical and scientific nature that, articulated under a series of procedures and technical methods, are applied to meet the needs of individuals. The Dictionary of the Royal Spanish Academy defines it as: “Group of instruments, technical resources or procedures used in a certain field or sector.” (Royal Spanish Academy, 2018)

From the point of view of learning it is worth mentioning that algorithmic learning in Mathematics has played an important role, where an algorithm is understood as a finite series of rules to be applied in a specific order to a finite number of data to arrive at a certain number result (that is, without indeterminacy or ambiguities), in a finite number of steps, each of which is only an instruction.

However, in recent times, heuristic-based learning, defined by Müller (1987), has been preferred as:

… A scientific discipline applicable in all sciences and includes the elaboration of principles, strategies, rules and programs that facilitate the search for ways to solve

problems, that is, for non-algorithmic tasks of any kind and of any scientific domain or practical. (p. 8)

On the other hand, Müller (1987) proposes heuristic procedures as a scientific method, which can be divided into principles, rules and strategies.

Heuristic principles: they constitute suggestions to find - directly - the idea of solution; it makes possible, therefore, to determine both the means and the solution way.

Within these principles, analogy and reduction (modeling) stand out.

Heuristic rules: they act as general impulses within the search process and help to find, especially, the means to solve the problems.

Heuristic strategies: they behave as organizational resources of the resolution process, which especially contribute to determining the solution to the problem addressed Barrows (1986) defines problem-based learning (ABP) as "a learning method based on the principle of using problems as a starting point for the acquisition and integration of new knowledge" (p. 17). In this methodology the protagonists of learning are the students themselves, who assume the responsibility of being an active part in the process. There are several general theories that support the teaching-learning process of Mathematics, and by extension also the inclusion of ICT. It can be mentioned for example the behaviorism, which has its origin in the experiments that psychologists such as Petrovich, Pavlov and Skinner performed with domestic animals. The most notable representatives of behaviorism are Thorndike, Burrhus and Skinner, and more recently Gagné. It is also worth mentioning Gestalt's theory, which is the perception of a complete structure or form as something more than simply the parts that constitute it. (Garcia, 2001)

No less important have been the psychological theories of cognitivism, where Broadben stands out, with his publication Perception and Communication, in 1958; and constructivism, pedagogical current created by Ernest von Glasersfeld based on the theory of constructivist knowledge, which postulates the need to provide students with tools that allow them to create their own procedures to solve a problematic situation.

One of the most important and valid theories in recent times is the socio-historical-cultural theory of Vygotsky (1934), whose work began to be known and appreciated in the western world around 1960 and that with the publication of Krutetski (1976) served to popularize these ideas in the field of mathematics teaching. The socio-historical-cultural theory arose from the work of Vygotsky (1934), in response to behaviorism his main idea is based on the fact that the most important contribution to individual cognitive development comes from society and relationships between individuals.

Integration of ICT in the teaching-learning process of School Mathematics

ICTs offer possibilities for adapting teaching to the special needs of each student, those who are easily distracted can focus more intensely on tasks with computers; those with organizational difficulties can benefit from the restrictions imposed by their environment and, students with physical disabilities radically increase their mathematical possibilities with special technologies.

For ICTs to be an essential part of math classes, they must be selected and used in ways that are compatible with the educational objectives, with the characteristics of the students and their way of learning individually.

The teaching - learning process of Mathematics requires a substantial change in the way it develops and in the expected results of the students. The use of ICTs does not definitively solve the pedagogical gaps and conceptual deficiencies that are presented to students when they study the subject, but they do constitute an important option to start generating positive transformations.

In that sense, importance should be given to developer learning, where (González and García, 2012) state that:

to direct the learning of students with a developer approach it is necessary to consider that the current class must transform the student's participation in the search and application of knowledge from a passive position to an active position, a teaching that leads to the development of potentialities in the student (p. 72)

This research assumes the term virtual education given by Loaiza where he states that:

virtual education is an educational strategy that facilitates the management of information and allows the application of new pedagogical methods focused on the development of significant learning, which are focused on the student and active participation. It allows to overcome the quality of face-to-face resources, adjusts to the personal schedule of students and facilitates continuous interaction between classmates and the teacher through virtual means. (2002, p. 32)

ICTs are a resource for exploration and visualization, they are important in mathematical teaching, as the student through them can establish relationships among mathematical objects and can become familiar with them, making them tangible, observable and manipulable, as an advantage over traditional teaching. where generally these objects are more abstract.

Virtual Learning Environments

Many terms related to virtuality have emerged such as: Virtual Learning Environment (VLE), Learning Object (LO), Virtual Learning Object (VLO), Virtual Information Object (VIO), Virtual Teaching and Learning Environment (VTLE), and others. It is not an objective of this research, to theorize about the terminologies used, however, the large number of definitions given by various authors, some even conflicting. However, it is important to assume a critical position regarding the concepts that will be addressed in this study to avoid conceptual ambiguities.

The Colombian National Ministry of Education developed and assumed its own definition of Learning Object:

an Object of Learning is a set of digital resources, self-contained and reusable for an educational purpose and consisting of at least three internal components: content, learning activities and contextualization elements. The Learning Object must have an external information structure (metadata) that facilitates its storage, identification and recovery. (Ministry of National Education, 2006)

However, this definition has the disadvantage that it refers to the Learning Object (LO) as something “virtual” when it is not necessarily so, for example, García (2005) states that:

A learning object may consist of a more or less complex question or a similar tone response, an image or simulation; exercises, questionnaires or diagrams can also be a learning object, as well as a slide or set of them; a table, experiments, games or animations; a video or audio sequence, some sentences or paragraphs of a text, part of a lesson; some computer applications -Flash, PowerPoint, Java, Applets ... -; case studies, URLs, etc. That is, objects can acquire very different shapes and be presented in different formats and media. (p. 1)

As you can see, not all learning objects are virtual, in fact, the first ones used in teaching were tangible, real objects. For this reason, the definition of the Colombian National Education Ministry is preferred, but not for (LO) but for Virtual Learning Objects (VLO).

The Dictionary of the Spanish Language (2018), defines the word environment as:

"Environment, what surrounds" and also as: "Set of characteristics that define the place and the way of execution of an application".

It also defines the word environment as:

"That surrounds something or someone as an element of their environment", hence many authors use interchangeably as Virtual Learning Environments and Virtual Learning Environments in the space where this virtual education takes place.

Suárez (2002), defines EVA as: “an action system that bases its particularity on an educational intention and on a specific way to achieve it through info-virtual resources” (p. 32), for its part Dillenbourg (2000) distinguishes VLE such as:

a space where the characteristics in which the information is provided is designed, the stated environment must be social where the virtual space is a representation and the students are active actors, multiple tools are integrated and this virtual environment overlaps with the physical environment. (p. 12)

Osorio (2012) states that:

Virtual Learning Environment is a space in which there is a pedagogical process mediated by technologies. Virtual environments become systems in which the

didactics, tools and resources that teachers use with students, whether virtual or face-to-face, are compiled. (p. 12)

For this reason, the term Virtual Learning Environment (VLE) is preferred, to define that space to carry out the pedagogical process mediated by technology.

B-learning as a teaching-learning methodology

Blendedlearning or b-learning is understood as the organic integration of face-to-face approaches and virtuality in education. This methodology is based on the needs of education in the current era by merging the face-to-face and virtual communicationally (Garrison and Vaughan, 2013).

The blendedlearning makes possible the use of technologies in a classroom, while generating several mixed moments or integration during the educational process. Face-to-face activities are stimulated and motivated by the use of ICT, while stimulating knowledge management outside the classroom. The possibility of combining both teaching methods, (face-to-face and virtual) makes the advantages of each one take advantage and a greater impact on the learning of new students in the twenty-first century.

Lin et al. (2017), suggest that traditional teaching complemented with computer-assisted teaching methods can be used in the teaching-learning process of mathematics in high school.

In the teaching and learning of mathematics, students sometimes face difficult problems to solve in a face-to-face environment, where using technology maximizes their time and solution.

An investigation developed by Herrera and Montaña (2015), “Problem-based learning supported in b-learning environments as a teaching strategy to improve the academic performance of students in higher education” with the use of a quantitative methodology of basic type and applying a descriptive correlational approach, obtained as a result that problem-based learning constitutes an important support in semipresence or b-learning environments.

Manjarres and Chiappe (2012) carry out the research “Incidence of a Blended learning environment, in the transformation of mathematical competences in university students”, which is a case study of qualitative approach. The results obtained in the research allowed to identify some transformations in the students, especially in their ability to solve problems, abilities to communicate orally and in writing and in the ability to apply mathematical knowledge to the field of Civil Engineering.

For his part, Córdova (2016) in his master's thesis "B-learning and the development of mathematical thinking in 11th grade students of the José Elías Puyana Industrial Technical College, Colombia (2015)" states that there is a positive Moderate and significant relationship between blendedlearning and mathematical communication, in addition to positive and significant between blendedlearning with mathematical reasoning, positive and significant between blendedlearning with mathematical thinking in 11th grade students.

It is also important to select the appropriate computer tools to carry out the task of educating students through the b-learning methodology. An important example is the use of the Moodle platform, due to the advantages it offers and because its work philosophy is consistent with the socio-historical-cultural paradigm. Several researches have shown the benefits of using Moodle in secondary education, such as: (Kok, 2008; White, 2010; Lu and Law, 2011); who argue that Moodle had pedagogical advantages since it was built according to the teaching approach that emphasizes the construction of knowledge through active and interactive learning, and learning of multisensory experience through multimedia.

Conclusions

It is necessary for teachers to continue conducting research that allows a more effective use of technological resources in the teaching-learning process of School Mathematics. The diversity of studies, with different methodologies, demonstrate that fair teaching must be adapted to the individual characteristics of each student.

Bibliographic references

Ángel, J., y Castiblanco, S. (2019). Efectividad del b-learning sobre rendimiento académico y retención en estudiantes en educación a distancia.

Entramado

, (1), 212-22.

Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D. y Thomas, K. (1996).

A Framework for Research and Development in Ungraduate Mathematics education.

Research in CollegiateMathematicsEducation

1 – 32.

Balladares Burgos, J. A. (2017).

Educación digital y formación del profesorado en modalidad semipresencial y virtual (b-learning y e-learning). Estudios de caso

. Recuperado de

http://dehesa.unex.es/bitstream/handle/10662/6072/TDUEX_2017_Balladares_Burgos.pdf?sequence=1&isAllowed=y

Barrows, H. S. (1986). A Taxonomy of problembased learning methods.

Medical Education,20

, 481-486.

Córdova, Y. A. (2016).

El b-learning y el desarrollo del pensamiento matemático en los estudiantes de 11° grado del Colegio Técnico Industrial José Elías Puyana, Colombia

. Tesis presentada al grado de Magíster en Informática Educativa. Lima, Perú. Recuperado de:

http://repositorio.uwiener.edu.pe/bitstream/handle/123456789/1095/MAESTRO%20-%20C%C3%B3rdoba%20Buitrago%2C%20Yolvi%20Adriana.pdf?sequence=1&isAllowed=y

Cruz Pichardo, I. M., y Puentes Puente, A. (2012). Innovación educativa: Uso de las TIC en la enseñanza de la matemática básica.

Revista de Educación Mediática y TIC

(2), 127-145.

Dillenbourg, P. (2000).

Virtual learning environments, Workshop on virtual learning

Recuperado de http://tecfa.unige.ch/tecfa/publicat/dil-papers-2

Dubinsky, E. (1996). Aplicación de la Perspectiva piagetana a la Educación Matemática Universitaria.

Educación Matemática

(3), 24-41.

Faustino, A., y Pérez, S. (2013). Utilización de las TIC en la enseñanza de la estadística en la Educación Superior Angolana.

Revista de Ciencias Sociales

(2), 0-31.

García Aretio, L. (2005). Objetos de aprendizaje. Características y repositorios.

Boletín Electrónico de Noticias de Educación a Distancia

, 2–5. Recuperado de

http://www.tecnoeducativos.com/descargas/objetos_virtuales_deparedizaje.pdf

Garrison, D., y Vaughan, N. (2013). Institutional change and leadership associated with blended learning innovation: Two case studies.

The Internet and Higher Education

, 24–28. https://doi.org/10.1016/j.iheduc.2012.09.001

Godino, J. D. (2010).

Perspectiva de la Didáctica de las Matemáticas,

1–57. Recuperado de:

http://www.ugr.es/~jgodino/fundamentos_teoricos/perspectiva_ddm.pdf%0Ahttp://www.ugr.es/~jgodino/

González Polo, M., y González, L. A. (2012). Procedimientos didácticos para la dirección de un aprendizaje desarrollador,

EduSol

, 12, 71-82.

Herrera, A. (2015).

Aprendizaje Basado en Problemas, una visión actual para la enseñanza de la Enfermería.

[tesis]. Bogotá, Colombia: Universidad Nacional de Colombia. Recuperado de

http://www.bdigital.unal.edu.co/11418/1/04868240.2013.pdf

Lancheros, S. (2014).

Aplicación de un modelo de clase b-learning para el aprendizaje de la Matemática.

Recuperado de

http://www.ilae.edu.co/Ilae_Files/Libros/20141102101656131112996.pdf

Lin, Y. W., Tseng, C. L., y Chiang, P. J. (2017). The effect of blended learning in mathematics course. Eurasia Journal of Mathematics.

Science and Technology Education

(3), 741–770. Recuperado de

https://doi.org/10.12973/eurasia.2017.0064

Lu, J., y Law, N. W. Y. (2011).

Understanding collaborative learning behavior from Moodle log data.

Interactive Learning Environments

(5), 451-466.

Manjarrés García, G. A., y Chiappe Laverde, A. (2012).

Incidencia de un ambiente virtual de aprendizaje, como apoyo a la presencialidad, en las transformaciones de las competencias matemáticas en estudiantes universitarios

. Artículo para obtener el título de magister en informática educativa. Recuperado de

https://intellectum.unisabana.edu.co/bitstream/handle/10818/5125/129957.pdf?sequence=1&isAllowed=y

Melo Ospina, L., y García González, L. (2018). Pensamiento Complejo y rendimiento académico en la asignatura Lógica de programación carrera Ingeniería de sistemas en la Escuela Tecnológica, Instituto Técnico Central. En

Educación y aprendizaje: perspectivas y escenarios actuales en la educación digital,

1ra ed. [online] La Habana: Editorial Universitaria. Recuperado de:

http://eduniv.mes.edu.cu/bd/eduniv/Southwell%2C%20Myriam/Educacion%20y%20aprendizaje_%20perspectiva%20%2826%29/Educacion%20y%20aprendizaje_%20perspe%20-%20Southwell%2C%20Myriam.pdf

Ministerio de Educación Nacional, Colombia. (2017

Derechos Básicos de Aprendizaje

. Recuperado de

http://aprende.colombiaaprende.edu.co/sites/default/files/naspublic/DBA_Matemáticas.pdf

Molina, R. (2017).

Relación entre entornos virtuales de aprendizaje y estilos de aprendizaje en la formación de magísteres con metodología virtual

. Recuperado de

http://recursos.portaleducoas.org/sites/default/files/5066.pdf

Müller, H. (1987). El programa heurístico general para la resolución de ejercicios. En Boletín

Sociedad Cubana de Matemática

, (9), La Habana.

Osorio, M. (2012).

Unidad 1: Globalización, Tecnología, Sociedad del Conocimiento y Tecnologías de la Información y la Comunicación (TIC): Aproximaciones para situar el binomio educación-tecnología en el

contexto

mundial actual

. En curso virtual Asesoría para el uso de las TIC en la formación.

Bogotá: SENA.

NCTM (2000).

Principles and Standards for School Mathematics

. Reston, VA: NCTM.

Real Academia Española:

Diccionario de la lengua española

, 23.ª ed., [versión 23.2 en línea].

(2019). Recuperado de https://dle.rae.es

Tapscott, D. (2009).

Grown up digital: How the Net generation is changing your world

New York: McGraw Hill.

Unesco (2013).

Enfoques estratégicos sobre las TICS en educación en América Latina el Caribe.

Santiago de Chile: Unesco.

Wellings, J., y Levine, M. (2009).

The Digital Promise: Transforming Learning with Innovative Uses of Technology

Recuperado de http://dmlcentral.net/ sites/dmlcentral/files/resource_files/Apple. pdf

White, B. (2010). Using ICT to enhance curriculum opportunities for students in rural and remote schools.

Australian Educational Computing

(2), 27-30.

Zambrano, y Areque (2016).

Blended Learning ¿Combination, integration or convergence?

Recuperado de

https://www.researchgate.net/publication/310843532_Blended_Learning_Combinacion_Integracion_o_Convergencia

Luis Alberto García González; Armando Solano Suarez: Mathematics Teaching mediated by technology

PAGE \* MERGEFORMAT2

EduSol Vol. 20. Núm.70