Improved version of TeacherCollection design

IIndexedTeacherCollection.cs

namespace DotConnect.LeakyAbstraction
{
    public interface IIndexedTeacherCollection
    {
        int GetIndex(string teacherName);
    }
}

ITeacherCollection.cs

using System.Collections.Generic;

namespace DotConnect.LeakyAbstraction
{
    public interface ITeacherCollection : IEnumerable<Teacher>
    {
        ITeacherCollection WhereTeachMathematics();
        ITeacherCollection WhereExperienced();
        int Count{get;}
        IIndexedTeacherCollection BuildIndex();
    }
}

Program.cs

using System;
using System.Linq;

namespace DotConnect.LeakyAbstraction
{
    class Program
    {
        static void Main(string[] args)
        {
            var school = new School
            {
                Name = "Gotham City"
            };
            school.Teachers.Add(new Teacher
            {
                Name = "Batman",
                Specialty = "Mathematics",
                StartedOn = DateTime.Now.AddYears(-11),
                IsStillAtWork = true
            });
            school.Teachers.Add(new Teacher
            {
                Name = "Joker",
                Specialty = "Chemical",
                StartedOn = DateTime.Now.AddYears(-6),
                IsStillAtWork = false
            });
            Console.WriteLine("Total teachers: {0}", school.TeacherCollection.Count);
            Console.WriteLine("Mathematics teachers are: {0}",
                string.Join("; ", school.TeacherCollection
                                        .WhereTeachMathematics()
                                        .Select(x => x.Name)));
            Console.WriteLine("> 10 years teachers are: {0}",
                string.Join("; ", school.TeacherCollection
                                        .WhereExperienced()
                                        .Select(x => x.Name)));
            var batmanIndex = school.TeacherCollection.BuildIndex().GetIndex("Batman");
            Console.WriteLine($"Hey Batman is at {batmanIndex}");
        }
    }
}

TeacherCollection.cs

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

namespace DotConnect.LeakyAbstraction
{
    public class TeacherCollection : ITeacherCollection, IIndexedTeacherCollection
    {
        private readonly IList<Teacher> _teachers = new List<Teacher>();

        public TeacherCollection(IEnumerable<Teacher> teachers)
        {
            if (teachers != null)
                _teachers = teachers.Where(x => x.IsStillAtWork).ToList();
        }

        public ITeacherCollection WhereTeachMathematics()
        {
            return new TeacherCollection(_teachers.Where(x => x.Specialty == "Mathematics"));
        }

        public ITeacherCollection WhereExperienced()
        {
            return new TeacherCollection(_teachers.Where(x => DateTime.Now >= x.StartedOn.AddYears(10)));
        }

        public IEnumerator<Teacher> GetEnumerator()
        {
            return _teachers.GetEnumerator();
        }

        IEnumerator IEnumerable.GetEnumerator()
        {
            return _teachers.GetEnumerator();
        }

        public int Count
        {
            get { return _teachers.Count; }
        }

        public int GetIndex(string teacherName)
        {
            for(var index = 0; index < _teachers.Count; index ++)
            {
                if(_teachers[index].Name == teacherName)
                {
                    return index;
                }
            }
            return -1;
        }

        public IIndexedTeacherCollection BuildIndex()
        {
            return new TeacherCollection(_teachers.OrderBy(x => x.StartedOn));
        }
    }
}