Quarterback Jarrett Stidham practices with the Patriots on Wednesday for the first time since August, when he went on injured reserve following back surgery. Steven Senne/Associated Press

FOXBOROUGH, Mass. — The New England Patriots are caught between the team they are and the team they want to be.

They know they’re 2-4, but they insist that record doesn’t reflect how good they are.

“I think we’re a good team with a bad record right now,” special teams ace Justin Bethel said after Sunday’s loss to Dallas.

Tight end Jonnu Smith repeated the sentiment Wednesday.

“We’re 2-4. We know that we’re not a 2-4 team,” Smith told reporters. “I think we just have to continue to come in here with the work mindset, which we have.”

Of course, the prevailing wisdom in the NFL about a team’s character is best summarized by what former Pats coach Bill Parcells once famously declared: “You are what your record says you are.”

Last season, with his team mired 4-6, Coach Bill Belichick offered a similar refrain when asked about whether the Patriots were better than their record.

“Our record is our record,” he said last November.

On Wednesday, after Smith asserted the Pats aren’t a typical 2-4 team, Belichick was asked if he agreed. He deflected by offering an answer that seemed more directed at his tight end than the media.

“Well, we’re getting ready for the Jets here,” Belichick said, “so (let’s) just try to focus on what we can do, and be ready to go this week and try to go out there and play a good football game.”

QUARTERBACK JARRETT STIDHAM and defensive tackle Byron Cowart participated in their first regular-season practice Wednesday, indicating one or both could be added to the active roster sometime within the next three weeks.

Cowart opened training camp on the PUP list with an undisclosed injury and has remained there ever since. The Pats placed Stidham on PUP after he underwent back surgery in early August. The team must either activate Cowart and/or Stidham to the 53-man roster or leave them on the PUP list, where they would be sidelined for the rest of the season.

Cowart’s return may prove timely, with starting nose tackle Davon Godchaux missing practice Wednesday. Stidham’s future role with the team is cloudier unless he can prove he’s an appreciably better than veteran Brian Hoyer, who is Mac Jones’ top backup and mentor. Over 48 career pass attempts, Stidham has completed 50% his throws for 256 yards, two touchdowns and three picks.

Journeyman quarterback Garrett Gilbert is also their practice squad.

PRACTICE REPORT: The New England Patriots were without several key defensive players during Wednesday’s practice as the team’s injury issues continue to grow.

Defensive starters listed as non-participants Wednesday include defensive lineman Davon Godchaux (finger), linebacker Dont’a Hightower (elbow/ankle) and defensive lineman Deatrich Wise (knee). On top of that, defensive back Jonathan Jones, who’s played over 50% of defensive snaps this season, was also absent due to a knee injury. CB Shaun Wade remains out due to a concussion.

Hightower was not listed on the injury report last week and played 71% of the team’s defensive snaps against the Cowboys. Jones missed time in the second quarter with a ribs injury, but returned to play. Wade hasn’t practiced in two weeks. Godchaux’s absence is another mystery. The 330-pound run stuffer played 63% of the Pats’ defensive snaps last Sunday.

Elsewhere, the Patriots had a long list of players limited in practice due to injury, with defensive lineman Christian Barmore (shoulder), defensive back Adrian Phillips (back) and linebacker Ja’Whaun Bentley (ribs) among those popping up on the injury report with new injuries.

Starting offensive lineman Shaq Mason returned to practice late last week but did not play in Sunday’s game against the Cowboys. He remains limited in practice.

BRIAN POOLE, former cornerback with the Jets, was working out for the Patriots on Wednesday, according to reports.

Poole, 28, played the last two seasons with the Jets and signed with the Saints this summer but quickly landed on injured reserve and was released last week. In New York, he grabbed three interceptions and allowed an opposing passer rating of 80.8. Poole primarily played in the slot and on special teams.

The 5-foot-9, 210-pound corner entered the league with the Falcons as an undrafted free agent in 2016. He started nine of 16 games his rookie season and played two more seasons in Atlanta. With the Falcons, Poole recorded four interceptions, two fumble recoveries and 196 tackles.

His addition would give the Patriots needed corner depth, after the team signed second-year defensive back Myles Bryant from its practice squad to the active roster Tuesday.

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